M L Aggarwal Solutions for Chapter: Triangles, Exercise 8: Chapter Test

In the adjoining figure, $OA\perp OD, OC\perp OB, OD=OA$ and $OB=OC$. Prove that $AB=CD$.

In the adjoining figure, $AB\parallel DC$. $CE$ and $DE$ bisects $\angle BCD$ and $\angle ADC$ respectively. Prove that $AB=AD+BC$.

In $△ABC, D$ is a point on $BC$ such that $AD$ is the bisector of $\angle BAC$. $CE$ is drawn parallel to $DA$ to meet $BA$ produced at $E$. Prove that $△CAE$ is isosceles.

In the adjoining figure, $ABC$ is a right-angled triangle at $B$. $ADEC$ and $BCFG$ are squares. Prove that $AF=BE$.

In the adjoining figure, $BD=AD=AC$. If $\angle ABD=36°$, find the value of $x$.

In the adjoining figure, $TR=TS, \angle 1=2\angle 2$ and $\angle 4=2\angle 3$. Prove that $RB=SA$.

In the adjoining figure, $AP\perp l$ and $PR>PQ$. Show that $AR>AQ$.

If $O$ is any point in the interior of a triangle $△ABC$, show that $OA+OB+OC>\frac{1}{2}\left(AB+BC+CA\right)$.