J P Mohindru and Bharat Mohindru Solutions for Chapter: Triangles, Exercise 6: EXERCISE

Given a $△ABC$, in which $\angle B=90°$ and $AB=\sqrt{3}BC$. Prove that $\angle C=60°$.

$△ABC$ is right-angled at $B$, $D$ is the midpoint of $BC$. Prove that $A{C}^2=4A{D}^2-3A{B}^2$

$△ABC$ is an isosceles triangle, right-angled at $C$. Prove that $A{B}^2=2A{C}^2$. 

In a quadrilateral$ABCD,$ $\angle B=90°, A{D}^2=A{B}^2+B{C}^2+C{D}^2$. Prove that $\angle ACD=90°$.

Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.

Prove that sum of square of sides of a rhombus is equal to the sum of squares of its diagonals.

$P$ and $Q$ are two points on the sides $CA$and $CB$ respectively of $△ABC$ right angled at $C$. Prove that: $A{Q}^2+B{P}^2=A{B}^2+P{Q}^2$.

In an equilateral $△ABC$, $D$ is a point on side$BC$, such that$BD=\frac{1}{3}BC$. Prove that $9A{D}^2=7A{B}^2$.