Amit M Agarwal Solutions for Chapter: Properties of Triangles, Heights and Distances, Exercise 2: Work Book Exercise 10.2

If $a^2, b^2, c^2$ are in $\mathrm{A}.\mathrm{P}.$, then $\cot A, \cot B$ and $\cot C$ are in

Given an isosceles triangle, whose one angle is $120°$ and radius of its incircle is $\sqrt{3}$. Then, the area of the triangle $(\mathrm{in} \mathrm{sq} \mathrm{units})$ is

A regular polygon of nine sides, each of length $2$, is inscribed in a circle. The radius of the circle is

In a $\mathrm{\Delta }ABC, \sin A+\sin B+\sin C=1+\sqrt{2}$, $\cos A+\cos B+\cos C=\sqrt{2},$ if the triangle is

A circle is inscribed in an equilateral triangle of side $a$. The area of any square inscribed in the circle is

In a $∆ABC$, the line joining the circumcentre to the incentre is parallel to $BC,$ then $\cos B+\cos C$ is equal to

The exradii of a triangle $r_1, r_2$ and $r_3$ are in harmonic progression, then the sides $a, b \& c$ are in

In an equilateral triangle, the inradius and the circumradius are connected by