Properties of Triangles PYQs - Last 10 Years

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Practice 88 AP EAPCET Mathematics questions from Properties of Triangles. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 10 Years Properties of Triangles Questions

Showing 50 of 88 filtered questions.

1Properties Of Triangles

If in $\triangle A B C, B=45^{\circ}, a=2(\sqrt{3}+1)$ and area of $\triangle A B C$ is $6+2 \sqrt{3}$ sq. units, then the side $b=$

2Properties Of Triangles

In a $\triangle A B C$, if $\sin ^2 B=\sin A$ and $2 \cos ^2 A=3 \cos ^2 B$, then the triangle is

3Properties Of Triangles

In $\triangle A B C$, if $A, B, C$ are in arithmetic progression, then
\(\sqrt{a^2-a c+c^2} \cdot \cos \left(\frac{A-C}{2}\right)=\)

4Properties Of Triangles

In a $\triangle A B C, 2 A+C=300^{\circ}$. If the circumradius of the $\triangle A B C$ is eight times its inradius, then $\sin \frac{C}{2}=$

5Properties Of Triangles

In $\triangle A B C$, if $C=120^{\circ}, c=\sqrt{19}$ and $b=3$, then $a=$

6Properties Of Triangles

In $\triangle A B C$, if $a=5, b=4$ and $\cos (A-B)=\frac{31}{32}$, then $c=$

7Properties Of Triangles

In $\triangle A B C$ is the line joining the circumcentre and the incentre is parallel to $B C$, then $\cos B+\cos C=$

8Properties Of Triangles

In a $\triangle A B C$, if $r_1: r_2=3: 4$ and $r_2: r_3=2: 3$, then $a:\(b:\)c$=

9Properties Of Triangles

In a $\triangle A B C$, if $A=30^{\circ}$ and $\frac{b}{(\sqrt{3}+1)^2+2(\sqrt{2}-1)} =\frac{c}{(\sqrt{3}+1)^2-2(\sqrt{2}-1)}$, then $B$

10Properties Of Triangles

In a $\triangle A B C$, if $a, b, c$ are in arithmetic progression and the angle $A$ is twice the angle $C$, then $\cos A: \cos B: \cos C=$

11Properties Of Triangles

In a $\triangle A B C, \frac{2\left(r_1+r_3\right)}{a c(1+\cos B)}=$

12Properties Of Triangles

In a $\triangle A B C, A, B$ and $C$ are in arithmetic progression, $r r_3=r_1 r_2$ and $c=10$, then $a^2+b^2+c^2=$

13Properties Of Triangles

In $\triangle A B C$ if $\cos A \cos B+\sin A \sin B \sin C=1$, then $\sin A+\sin B+\sin C=$

14Properties Of Triangles

In $\triangle A B C$, if $a=6, b=8$ and $c=10$, then $\frac{2 r_2 r_3}{r r_1}=$

15Properties Of Triangles

In $\triangle A B C$, if $a: b: c=4: 5: 6$, then $\frac{\cos A+3 \cos C}{\cos B}=$

16Properties Of Triangles

In $\triangle A B C$, if $a=13, b=8, c=7$, then $\cos (B+C)=$

17Properties Of Triangles

In $\triangle A B C$, if $a=8, b=10, c=12$, then $\frac{r}{R}=$

18Properties Of Triangles

If the median $A D$ of the $\triangle A B C$ is bisected at $E$ and $B E$ meets $A C$ in $E$, then $A F: A C=$

19Properties Of Triangles

In a $\triangle A B C$, if $\left(r_1-r_3\right)\left(r_1-r_2\right)-2 r_2 r_3=0$, then $a^2-b^2=$

20Properties Of Triangles

If $A(0,0,0) B(3,4,0)$ and $C(0,12,5)$ are the vertices of a $\triangle A B C$, then the $x$-coordinate of its incentre is

21Properties Of Triangles

In a $\triangle A B C, A-B=120^{\circ}, R=8 r$, then $\frac{1+\cos C}{1-\cos C}=$

22Properties Of Triangles

In $\triangle A B C, \sqrt{\frac{r \cdot r_2}{r_3 r_1}}=$

23Properties Of Triangles

In $\triangle A B C$, if $r=3$ and $R=5$, then $\frac{1}{a b}+\frac{1}{b c}+\frac{1}{c a}=$

24Properties Of Triangles

If the sides $a, b, c$ of the $\triangle A B C$ are in harmonic progression, then $\operatorname{cosec}^2 A / 2, \operatorname{cosec}^2 B / 2, \operatorname{cosec}^2 C / 2$ are in

25Properties Of Triangles

In a $\triangle A B C$, if $\sin \frac{A}{2}=\frac{1}{4} \sqrt{\frac{3}{5}}, a=2, c=5$ and $b$ is an integer, then the area (in sq. units) of $\triangle A B C$ is

26Properties Of Triangles

In a $\triangle A B C$, if $r_1=3, r_2=4, r_3=6$, then $b=$

27Properties Of Triangles

In a $\triangle A B C$ if $a+c=5 b$, then $\cot \frac{A}{2} \cot \frac{C}{2}=$

28Properties Of Triangles

In $\triangle A B C$, the sum of the lengths of two sides is $x$ and the product of those lengths is $y$. If $c$ is the length of its third side and $x^2-c^2=y$, then the circumradius of that triangle is

29Properties Of Triangles

If the area of a $\triangle A B C$ is $4 \sqrt{5}$ sq units. Length of the side $C A$ is 6 units and $\tan \frac{B}{2}=\frac{\sqrt{5}}{4}$, then its smallest side is of length

30Properties Of Triangles

In a $\triangle A B C$ if $r_1=2 r_2=3 r_3$, then $a: b$ is

31Properties Of Triangles

In $\triangle A B C, a^2 \sin 2 B+b^2 \sin 2 A$ is equal to

32Properties Of Triangles

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

33Properties Of Triangles

\(\text { In } \triangle A B C, \frac{r_2\left(r_1+r_3\right)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}} \text { is equal to }\)

34Properties Of Triangles

In $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression $\Delta=\frac{\sqrt{3}}{2}$ and $r_1 r_2=r_2 r$, then $R=$

35Properties Of Triangles

In $\triangle A B C$, if $(a+c)^2=b^2+3 c a$, then $\frac{a+c}{2 R}=$

36Properties Of Triangles

In $\triangle A B C$, if $b+c: c+a: a+b=7: 8: 9$, then the smaller angle (in radians) of that triangle is

37Properties Of Triangles

In a $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression and $\cos A+\cos B+\cos C=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\tan A$ :

38Properties Of Triangles

In $\triangle A B C,\left(r_1+r_2\right) \operatorname{cosec}^2 \frac{C}{2}$ is equal to

39Properties Of Triangles

In a $\triangle A B C$, if $a=13, b=14$ and $c=15$, then $r_1=$

40Properties Of Triangles

In $a \triangle A B C$ if $r: R: r_2=1: 3: 7$, then $\sin (A+C)+\sin B$ is equal to

41Properties Of Triangles

If $(\alpha, \beta)$ is the orthocentre of the triangle with the vertices $(2,2),(5,1),(4,4)$, then $\alpha+\beta=$

42Properties Of Triangles

In a $\triangle A B C$, if $B C=5, C A=6$ and $A B=7$, then the length of the median drawn from $B$ onto $A C$ is

43Properties Of Triangles

In a $\Delta$ if the angles are in the ratio $3: 2: 1$, then the ratio of its sides is

44Properties Of Triangles

In $\triangle A B C$, if $A B: B C: C A=6: 4: 5$, then $R: r$ is equal to

45Properties Of Triangles

If 7 and 8 are the length of two sides of a triangle and $a^{\prime}$ is the length of its smallest side. The angles of the triangle are in AP and ' $a$ ' has two values $a_1$ and $a_2$ satisfying this condition. If $a_1 < a_2$, then $2 a_...

46Properties Of Triangles

In $\triangle A B C$, if $\left(r_2-r_1\right)\left(r_3-r_1\right)=2 r_2 r_3$, then $2(r+R)=$

47Properties Of Triangles

In $\triangle A B C$, if $a=13, b=14$ and $\cos \frac{C}{2}=\frac{3}{\sqrt{13}}$, then $2 r_1=$

48Properties Of Triangles

Match the items of List I with those of List II (here, $\Delta$ denotes the area of $\triangle A B C$ )

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49Properties Of Triangles

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

50Properties Of Triangles

If $O(0,0,0), A(3,0,0)$ and $B(0,4,0)$ form a triangle, then the incentre of $\triangle O A B$ is