Properties Of Triangles - Trigonometry - Mathematics Previous Year Questions

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

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

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 $b=$

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 $\frac{1}{p_1^2}+\frac{1}{p_2^2}+\frac{1}{p_3^2}=$

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 )

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

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, $\angle A B C$

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

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