Question 1: Palette 1/68

TS-EAMCET 2025 MCQ

If the angular bisector of the angle $A$ of the $\triangle A B C$ meets its circumcircle at $E$ and the opposite side $B C$ at $D$, then $D E \cos \frac{A}{2}=$

A

$\frac{a^2}{2(b+c)}$

B

$\frac{b^2}{c+a}$

C

$\frac{a}{b+c}$

D

$\frac{2 a}{a+b+c}$

Question 2: Palette 2/68

TS-EAMCET 2025 MCQ

In a $\triangle A B C, a=5, b=4$ and $\tan \frac{C}{2}=\sqrt{\frac{7}{9}}$, then its inradius $r=$

A

$\frac{\sqrt{7}}{2}$

B

$2 \sqrt{7}$

C

$\frac{9}{\sqrt{7}}$

D

$\frac{4}{\sqrt{7}}$

Question 3: Palette 3/68

TS-EAMCET 2025 MCQ

$y-x=0$ is the equation of a side of a $\triangle A B C$. The orthocentre and circumcentre of the $\triangle A B C$ are respectively $(5,8)$ and $(2,3)$. The reflection of orthocentre with respect to any side of the triangle lies on its circumcircle. Then, the radius of the circumcircle of the triangle is

A

5

B

$2 \sqrt{5}$

C

$\sqrt{10}$

D

$2 \sqrt{10}$

Question 4: Palette 4/68

TS-EAMCET 2025 MCQ

If $a=3, b=5, c=7$ are the sides of a $\triangle A B C$, then $\cot A+\cot B+\cot C=$

A

$\frac{15 \sqrt{3}}{4}$

B

$\frac{7}{\sqrt{3}}$

C

$\frac{83}{15 \sqrt{3}}$

D

$\frac{83 \sqrt{3}}{15}$

Question 5: Palette 5/68

TS-EAMCET 2025 MCQ

Let $p_1, p_2$ and $p_3$ be the altitudes of a $\triangle A B C$ drawn through the vertices $A, B$ and $C$ respectively. If $r_1=4$, $r_2=6, r_3=12$ are the ex-radii of $\triangle A B C$, then $\frac{1}{p_1^2}+\frac{1}{p_2^2}+\frac{1}{p_3^2}=$

A

$\frac{25}{72}$

B

$\frac{25}{144}$

C

$\frac{25}{288}$

D

$\frac{25}{216}$

Question 6: Palette 6/68

TS-EAMCET 2025 MCQ

If $a=3, b=5, c=7$ are the sides of a $\triangle A B C$, then its circumradius is

A

$\frac{7}{\sqrt{3}}$

B

$\frac{15}{2}$

C

$\frac{15 \sqrt{3}}{4}$

D

$\frac{\sqrt{3}}{2}$

Question 7: Palette 7/68

TS-EAMCET 2025 MCQ

Two ships leave a port at the same time. One of them move in the direction of $E 50^{\circ} \mathrm{N}$ with a speed of 8 kmph and the other moves in the direction of $\mathrm{S} 20^{\circ} \mathrm{E}$ with a speed of 12 kmph . Then, the distance between the ships at the end of 2 h is (in km )

A

$8 \sqrt{7}$

B

34

C

$8 \sqrt{19}$

D

32

Question 8: Palette 8/68

TS-EAMCET 2025 MCQ

In a $\triangle A B C$, if $c^2-a^2=b(\sqrt{3} c-b)$ and $b^2-a^2=c(c-a)$ then, $\angle A B C$

A

$30^{\circ}$

B

$60^{\circ}$

C

$45^{\circ}$

D

$90^{\circ}$

Question 9: Palette 9/68

TS-EAMCET 2025 MCQ

Let $A B C$ be a triangle right angled at $B$. If $a=13$ and $c=84$, then $r+R=$

A

42.5

B

169

C

98

D

48.5

Question 10: Palette 10/68

TS-EAMCET 2025 MCQ

In a $\triangle A B C$, if $r_1=4, r_2=8$ and $r_3=24$, then $a: b: c=$

A

$4: 7: 9$

B

$2: 3: 5$

C

$1: 2: 6$

D

$6: 2: 1$

Question 11: Palette 11/68

TS-EAMCET 2025 MCQ

In a $\triangle A B C,\left(r_2+r_3\right) \operatorname{cosec}^2\left(\frac{A}{2}\right)=$

A

$4 R \cot \left(\frac{A}{2}\right)$

B

$2 R \cot ^2\left(\frac{A}{2}\right)$

C

$\frac{4 R}{\tan ^2\left(\frac{A}{2}\right)}$

D

$\frac{2 R}{\tan \left(\frac{A}{2}\right)}$

Question 12: Palette 12/68

TS-EAMCET 2025 MCQ

If $p_1, p_2, p_3$ are the altitudes and $a=4, b=5, c=6$ are the sides of a $\triangle A B C$, then $\frac{1}{p_1^2}+\frac{1}{p_2^2}+\frac{1}{p_3^2}=$

A

$\frac{77}{225}$

B

$\frac{44}{225}$

C

$\frac{308}{225}$

D

$\frac{22}{75}$

Question 13: Palette 13/68

TS-EAMCET 2025 MCQ

Let the angles $A, B, C$ of a $\triangle A B C$ be in arithmetic progression. If the exradii $r_1, r_2, r_3$ of $\triangle A B C$ satisfy the condition $r_3^2=r_1 r_2+r_2 r_3+r_3 r_1$, then $b=$

A

$\frac{2 a}{\sqrt{3}}$

B

$\sqrt{2} a$

C

$\sqrt{3} a$

D

$a$

Question 14: Palette 14/68

TS-EAMCET 2024 MCQ

In a $\triangle A B C$, if $a=5, b=3, c=7$, then $\sqrt{\frac{\sin (A-B)}{\sin (A+B)}}=$

A

$\frac{4}{7}$

B

16

C

36

D

$\frac{4}{5}$

Question 15: Palette 15/68

TS-EAMCET 2024 MCQ

In a $\triangle A B C$, if $r_{1}=6, r_{2}=9, r_{3}=18$, then $\cos A=$

A

$\frac{5}{13}$

B

$\frac{4}{5}$

C

$\frac{5}{7}$

D

$\frac{7}{25}$

Question 16: Palette 16/68

TS-EAMCET 2024 MCQ

If $A B C$ is an isosceles triangle with base $B C$, then $r_{1}=$

A

$R^{2} \cos ^{2} A$

B

$\frac{a^{2}}{2}$

C

$\frac{r}{R}$

D

$R^{2} \sin ^{2} A$

Question 17: Palette 17/68

TS-EAMCET 2024 MCQ

In $\triangle A B C$, if $r_{1}+r_{2}=3 R, r_{2}+r_{3}=2 R$, then

A

$A B C$ is a right-angled isosceles triangle

B

$B=\frac{\pi}{3}$

C

$A=90^{\circ}, a \neq b \neq c$

D

$C=90^{\circ}, a: b: c=2: 1: \sqrt{3}$

Question 18: Palette 18/68

TS-EAMCET 2024 MCQ

In a $\triangle A B C$, the sides $b, c$ are fixed. In measuring angle $A$, if there is an error of $\delta A$, then the percentage error in measuring the length of the side $a$ is

A

$\frac{2 \Delta \delta A}{R \sin A} \times 100$

B

$2 \times \frac{\delta A}{A} \times 100$

C

$\frac{\Delta \delta A}{2 R^{2} \sin ^{2} A} \times 100$

D

$\frac{\Delta^{2} \delta A}{R \sin A} \times 100$

Question 19: Palette 19/68

TS-EAMCET 2024 MCQ

In triangle $A B C$, if $a=4, b=3$ and $c=2$, then $2(a-b \cos C)(a-c \sec B)=$

A

0

B

1

C

2

D

3

Question 20: Palette 20/68

TS-EAMCET 2024 MCQ

In $\triangle A B C$, if $A=45^{\circ}, C=75^{\circ}$ and $R=\sqrt{2}$, than $r=$

A

$\frac{3+\sqrt{3}}{\sqrt{3}+\sqrt{2}+1}$

B

$\frac{\sqrt{3}+1}{\sqrt{3}+\sqrt{2}+1}$

C

$\frac{\sqrt{3}+1}{\sqrt{6}+\sqrt{3}+3}$

D

$\frac{\sqrt{3}+1}{\sqrt{3}+\sqrt{2}}$

Question 21: Palette 21/68

TS-EAMCET 2024 MCQ

If $A(1,2,-3), B(2,3,-1)$ and $C(3,1,1)$ are the vertices of $\triangle A B C$, then $\left|\frac{-\cos A}{\cos B}\right|=$

A

$\frac{3 \sqrt{3}}{4 \sqrt{2}}$

B

$\frac{3 \sqrt{3}}{\sqrt{7}}$

C

$\frac{4 \sqrt{2}}{3 \sqrt{3}}$

D

$\frac{\sqrt{7}}{3 \sqrt{3}}$

Question 22: Palette 22/68

TS-EAMCET 2024 MCQ

If $A+B+C=2 S$, then $\sin (S-A) \cos (S-B)-\sin (S-C) \cos S=$

A

$\cos A \sin B \sin C$

B

$\sin A \cos B \cos C$

C

$\cos A \sin B$

D

$\sin A \cos B$

Question 23: Palette 23/68

TS-EAMCET 2024 MCQ

In a $\triangle A B C$, if $\tan \frac{A}{2}: \tan \frac{B}{2}: \tan \frac{C}{2}=15: 10: 6$, then $\frac{a}{b-c}=$

A

$\frac{8}{3}$

B

$\frac{7}{3}$

C

5

D

4

Question 24: Palette 24/68

TS-EAMCET 2024 MCQ

In a $\triangle A B C, \frac{a\left(r_1+r_2 r_3\right)}{r_1-r+r_2+r_3}=$

A

$\sqrt{\pi_1 r_2 r_3}$

B

$r_1 r_2+r_2 r_3+r_3 r_1$

C

$2(R+r)$

D

$2+\frac{r}{2 R}$

Question 25: Palette 25/68

TS-EAMCET 2024 MCQ

In a $\triangle A B C$, if $(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}=a^2+b^2$, then $\cos A=$

A

$\cos B$

B

$\sin B$

C

$\sin C$

D

$\cos C$

Question 26: Palette 26/68

TS-EAMCET 2024 MCQ

In a $\triangle A B C$, if $r_1 r_2+r_3=35, r_2 r_3+r_1=63$ and $r_3 r_1+r_2=45$, then $2 s=$

A

28

B

21

C

25

D

36

Question 27: Palette 27/68

TS-EAMCET 2023 MCQ

In $\triangle A B C$, if $a, b, c$ are in arithmetic progression and $A=2 C$, then $b: c=$

A

$4: 5$

B

$2: 3$

C

$5: 4$

D

$5: 6$

Question 28: Palette 28/68

TS-EAMCET 2023 MCQ

Assertion (A) In $\triangle A B C$, if $r=6, r_2=36, R=15$, then $c^2+a^2=b^2$.

Reason (R) In $\triangle A B C$, if $r: R: r_2=1: 2.5: 6$, then $B=90^{\circ}$. The correct option among the following is

A

Both (A) and (R) are true, (R) is a correct explanation of (A)

B

Both $(A)$ and $(R)$ are true, but $(R)$ is not a correct explanation of (A)

C

(A) is true and (R) is false

D

(A) is false and (R) is true

Question 29: Palette 29/68

TS-EAMCET 2023 MCQ

In $\triangle A B C$, if $a: b: c=4: 5: 6$, then the ratio of the circumradius to its inradius is

A

$16: 7$

B

$25: 11$

C

$5: 4$

D

$9: 5$

Question 30: Palette 30/68

TS-EAMCET 2023 MCQ

The perimeter of a $\triangle A B C$ is 6 times the arithmetic mean of the values of the sine of its angles. If its side $B C$ is of unit length, then $\angle A=$

A

$\frac{\pi}{6}$

B

$\frac{\pi}{3}$

C

$\frac{\pi}{2}$

D

$\pi$

Question 31: Palette 31/68

TS-EAMCET 2023 MCQ

In $\triangle A B C$, if $b=6, c=7$ and $\tan \frac{A}{2}=\frac{1}{\sqrt{6}}$, then the inradius of $\triangle A B C$ is

A

$\sqrt{\frac{2}{3}}$

B

$\frac{2 \sqrt{6}}{9}$

C

$\frac{\sqrt{2}}{9}$

D

$\frac{2 \sqrt{6}}{3}$

Question 32: Palette 32/68

TS-EAMCET 2023 MCQ

In $\triangle A B C$, if $a=7, b=8$ and $c=9$, then $\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}=$

A

$97 / 360$

B

$5 / 72$

C

$169 / 360$

D

$67 / 72$

Question 33: Palette 33/68

TS-EAMCET 2023 MCQ

In $\triangle A B C$, if $A$ is an acute angle, $b=6, c=9$ and $\sin A=\frac{2 \sqrt{14}}{9}$, then $3 a(\cos B+\cos C)=$

A

14

B

20

C

17

D

23

Question 34: Palette 34/68

TS-EAMCET 2023 MCQ

If the roots of the equation $x^3-11 x^2+36 x-36=0$ are the ex-radii of a $\triangle A B C$, then the perimeter of the $\triangle A B C$ is

A

24

B

18

C

12

D

9

Question 35: Palette 35/68

TS-EAMCET 2023 MCQ

$P Q R$ is an isosceles triangle with $P Q=P R$. If the radius of the circumcircle of $\triangle P Q R$ is equal to the length of $P Q$ then $\angle P=$

A

$30^{\circ}$

B

$60^{\circ}$

C

$45^{\circ}$

D

$120^{\circ}$

Question 36: Palette 36/68

TS-EAMCET 2023 MCQ

In $\triangle A B C$, if $\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos \cdot C}{c}$ and side $a=2$, then area of the $\triangle A B C$ (in sq units) is

A

$8 \sqrt{2}$

B

$4 \sqrt{3}$

C

$\sqrt{3} / 2$

D

$\sqrt{3}$

Question 37: Palette 37/68

TS-EAMCET 2023 MCQ

In an isosceles right angled triangle, a straight line is drawn from the mid-point of one of the equal sides to the opposite vertex. Then, a pair of possible values of the cotangents of the two angles so formed at that vertex are

A

1 and 2

B

2 and 3

C

3 and 4

D

4 and 5

Question 38: Palette 38/68

TS-EAMCET 2023 MCQ

In a $\triangle A B C$, if $r_1=2 r_2=3 r_3$, then $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}=$

A

$\frac{75}{60}$

B

$\frac{155}{60}$

C

$\frac{176}{60}$.

D

$\frac{191}{60}$

Question 39: Palette 39/68

TS-EAMCET 2022 MCQ

In $\triangle A B C$, if $a=7, b=8, \tan C=\frac{3 \sqrt{5}}{2}$ and $C$ is an acute angle, then $c=$

A

$\sqrt{145}$

B

5

C

11

D

9

Question 40: Palette 40/68

TS-EAMCET 2022 MCQ

In a $\triangle A B C$, if $\frac{a}{\tan A}=\frac{b}{\tan B}=\frac{c}{\tan C}$, then $\cos ^2 A+\cos ^2 B+\cos ^2 C=$

A

$\sqrt{2}$

B

$\frac{3}{4}$

C

$\frac{\sqrt{3}+1}{2}$

D

$\frac{2 \sqrt{3}-1}{2}$

Question 41: Palette 41/68

TS-EAMCET 2022 MCQ

In $\triangle A B C$, if $a=7, b=10$ and $c=11$, then $\frac{R}{r}=$

A

14

B

77

C

$\frac{24}{11}$

D

$\frac{55}{24}$

Question 42: Palette 42/68

TS-EAMCET 2022 MCQ

If $a, b$ and $c$ are the sides of $a \triangle A B C$ and $\left|\begin{array}{lll}b & 1 & a \\ a & 1 & c \\ c & 1 & b\end{array}\right|=0$, then $2(\cos A+\cos B+\cos C)=$

A

1

B

2

C

3

D

4

Question 43: Palette 43/68

TS-EAMCET 2022 MCQ

In $\triangle A B C$, if $A=\frac{\pi}{3}$ and $B=\frac{\pi}{4}$, then $\frac{a^2-b^2}{c^2}=$

A

$2-\sqrt{3}$

B

$2+\sqrt{3}$

C

$\sqrt{2}-1$

D

$\sqrt{2}+1$

Question 44: Palette 44/68

TS-EAMCET 2022 MCQ

In a $\triangle A B C$, if $a=3, b=7$ and $c=8$, then $\sin \frac{B}{2} \tan \frac{C-A}{2}=$

A

$\frac{15 \sqrt{3}}{22 \sqrt{7}}$

B

$\frac{5 \sqrt{2}}{11 \sqrt{7}}$

C

$\frac{5 \sqrt{3}}{11}$

D

$\frac{5 \sqrt{3}}{22}$

Question 45: Palette 45/68

TS-EAMCET 2022 MCQ

In a $\triangle A B C, A D$ and $B E$ are medians. If $A D=4, \angle D A B=\frac{\pi}{6}$ and $\angle A B E=\frac{\pi}{3}$, then the area of $\triangle A B C$ is

A

$\frac{14}{3 \sqrt{3}}$

B

$\frac{28}{3 \sqrt{3}}$

C

$\frac{11}{3 \sqrt{3}}$

D

$\frac{32}{3 \sqrt{3}}$

Question 46: Palette 46/68

TS-EAMCET 2022 MCQ

If $S$ is the circumentre of a $\triangle A B C, a=5, b=6, c=9$ and $S B=\frac{27}{4 \sqrt{2}}$, then $\sin 2 C=$

A

$\frac{4 \sqrt{2}}{9}$

B

$\frac{4 \sqrt{2}}{27}$

C

$\frac{-4 \sqrt{2}}{27}$

D

$\frac{-4 \sqrt{2}}{9}$

Question 47: Palette 47/68

TS-EAMCET 2022 MCQ

In a $\triangle A B C$, if $\frac{r}{r_1}=\frac{1}{2}$, then $4 \tan \frac{A}{2}\left(\tan \frac{B}{2}+\tan \frac{C}{2}\right)=$

A

1

B

2

C

3

D

4

Question 48: Palette 48/68

TS-EAMCET 2022 MCQ

If the sides of a $\triangle A B C$ whose perimeter is 42 are in arithmetic progression, its circumradius is $\frac{65}{8}$ and $B

A

$\frac{4}{13}$

B

$\frac{28}{65}$

C

$\frac{56}{65}$

D

$\frac{14}{65}$

Question 49: Palette 49/68

TS-EAMCET 2022 MCQ

In a $\triangle A B C$, if $a=7, c=11, \cos A=\frac{17}{22}$, $\cos C=\frac{1}{14}$, then $b \tan \frac{B}{2} \tan \frac{C-A}{2}=$

A

18

B

14

C

2

D

9

Question 50: Palette 50/68

TS-EAMCET 2022 MCQ

In any $\triangle A B C, r^2 \cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2}=$

A

$\Delta$

B

$2 \Delta$

C

$\Delta^2$

D

$5 \Delta$

Question 51: Palette 51/68

TS-EAMCET 2022 MCQ

In $\triangle A B C$, if $A$ is acute, $C$ is obtuse, $\sin A=\frac{3 \sqrt{3}}{14}, a=3$ and $b=5$, then $c=$

A

$16 / 7$

B

7

C

$14 / 3$

D

6

Question 52: Palette 52/68

TS-EAMCET 2022 MCQ

If $\Delta$ denotes the area of $\triangle A B C$, then $(b \sin C+c \sin B)(b \cos C+c \cos B)=$

A

$a b \cos C$

B

$2 \Delta$

C

$b c \cos A$

D

$4 \Delta$

Question 53: Palette 53/68

TS-EAMCET 2022 MCQ

Let $A$ be the area of in-circle and $A_1, A_2, A_3$ be the area of ex-circles of a triangle. If $A_1=4, A_2=9, A_3=16$, then $A=$

A

81

B

$\frac{61}{169}$

C

$\frac{144}{61}$

D

$\frac{144}{169}$

Question 54: Palette 54/68

TS-EAMCET 2022 MCQ

In a $\triangle A B C$, if $(b+c)^2 \sin ^2 \frac{A}{2}+(b-c)^2 \cos ^2 \frac{A}{2}=K(1-\cos 2 A)$, then $K=$

A

$R^2$

B

$2 R^2$

C

$R$

D

$2 R$

Question 55: Palette 55/68

TS-EAMCET 2022 MCQ

In a $\triangle A B C$, if $b=7, c=4 \sqrt{3}$ and $A=\frac{\pi}{6}$ then a $\sin B \sin C=$

A

$\frac{\sqrt{13}}{12}$

B

$\frac{\sqrt{13}}{7 \sqrt{3}}$

C

$\frac{12}{\sqrt{13}}$

D

$\frac{7 \sqrt{3}}{\sqrt{13}}$

Question 56: Palette 56/68

TS-EAMCET 2022 MCQ

In $\triangle A B C$, if $B C$ is the hypotenuse, then $r_2+r_3=$

A

$r_1+r$

B

$a$

C

$r-r_1$

D

$2(R+r)$

Question 57: Palette 57/68

TS-EAMCET 2020 MCQ

In a triangle $A B C$, if $a

A

3

B

4

C

2

D

6

Question 58: Palette 58/68

TS-EAMCET 2020 MCQ

In a triangle $A B C$, if $c=9, s=10$ and $\Delta=10 \sqrt{2}$ then $b\left[1+\sqrt{2} \tan \left(\frac{A-B}{2}\right)\right]=$

A

$a\left[1-\sqrt{2} \tan \left(\frac{A-B}{2}\right)\right]$

B

$C\left[1-\sqrt{2} \tan \left(\frac{A-B}{2}\right)\right]$

C

$a\left[\sqrt{2} \tan \left(\frac{A-B}{2}\right)-1\right]$

D

$C\left[\sqrt{2} \tan \left(\frac{A-B}{2}\right)-1\right]$

Question 59: Palette 59/68

TS-EAMCET 2020 MCQ

In a $\triangle A B C, \cot A+\cot B+\cot C=$

A

$\frac{a^2+b^2+c^2}{\Delta}$

B

$\frac{a+b+c}{4 \Delta}$

C

$\frac{a^2+b^2+c^2}{4 \Delta}$

D

$\frac{a^2+b^2+c^2}{2 \Delta}$

Question 60: Palette 60/68

TS-EAMCET 2020 MCQ

If the sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the area (in sq. units) of that triangle is

A

6

B

$\frac{15}{4} \sqrt{7}$

C

$\frac{18}{5} \sqrt{7}$

D

$\frac{14}{3} \sqrt{5}$

Question 61: Palette 61/68

TS-EAMCET 2020 MCQ

In $\triangle A B C, A D$ and $B E$ are medians drawn from $A$ and $B$. If $A D=\frac{7}{2}, \angle D A B=\frac{\pi}{8}$ and $\angle A B E=\frac{\pi}{4}$, then the area (in sq. units) of $\triangle A B C$ is

A

$\frac{7}{12}$

B

$\frac{49}{36}$

C

$\frac{49}{12}$

D

$\frac{7}{36}$

Question 62: Palette 62/68

TS-EAMCET 2020 MCQ

If the radius of the incircle of a triangle with sides $5 k, 6 k$ and $5 k$ is 6 , then the largest angle of that triangle is

A

$\cot ^{-1}\left(\frac{3}{7}\right)$

B

$\tan ^{-1}\left(\frac{24}{7}\right)$

C

$\sin ^{-1}\left(\frac{3}{5}\right)$

D

$\cos ^{-1}\left(\frac{6}{\sqrt{85}}\right)$

Question 63: Palette 63/68

TS-EAMCET 2020 MCQ

In a $\triangle A B C,\left(b^2-c^2\right) \cot A+\left(c^2-a^2\right) \cot B=$

A

0

B

$2 R^2[\sin 2 A-\sin 2 B]$

C

$\left(b^2-a^2\right) \cot (A+B)$

D

$2 R^2[\tan 2 A-\tan 2 B]$

Question 64: Palette 64/68

TS-EAMCET 2020 MCQ

In a $\triangle A B C, \frac{\Delta^2}{a^2+b^2+c^2}\left(\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}\right)=$

A

0

B

1

C

$\Delta$

D

S

Question 65: Palette 65/68

TS-EAMCET 2020 MCQ

If $R: r_1: r=5: 12: 2$, then $r+r_3+r_2-r_1=$

A

$\cos A$

B

$\sin A$

C

$2 r r_1$

D

$2 r_1^2 r$

Question 66: Palette 66/68

TS-EAMCET 2020 MCQ

In a $\triangle A B C$ if $\angle A=3 \angle B, C A=9$ and $B C=16$, then the length of $A B$ is

A

$\frac{5}{3}$

B

$\frac{7}{3}$

C

2

D

$\frac{35}{3}$

Question 67: Palette 67/68

TS-EAMCET 2020 MCQ

In $\triangle A B C, \frac{1+\cos C}{r_1+r_2}+\frac{1+\cos A}{r_2+r_3}+\frac{1+\cos B}{r_1+r_3}=$

A

$\frac{2}{3 R}$

B

$\frac{R}{2}$

C

$\frac{3}{2 R}$

D

$\frac{6 R}{5}$

Question 68: Palette 68/68

TS-EAMCET 2020 MCQ

In a triangle $A B C$, if $\cos A \cos B+\sin A \sin B \sin C=1$, then $a: b: c=$

A

$1: 1: \sqrt{2}$

B

$1: 1: 1$

C

$\sqrt{2}: 1: 1$

D

$1: \sqrt{2}: 1$