J P Mohindru and Bharat Mohindru Solutions for Chapter: Circles, Exercise 6: CHAPTER TEST

In the fig. the sides of $△ABC$ inscribe a circle. $AB=7 \mathrm{cm}, BC=8 \mathrm{cm}$ and $AC=9 \mathrm{cm}$. Find the lengths of $AP, BQ$ and $CR$.

In the figure, $l$ is a line intersecting the two concentric circles whose common centre is $O$, at the points $A, B, C$ and $D$. Show that $AB=CD$.

Two tangents $PA$ and $PB$ are drawn to the circle with centre $O$ such that $\angle APB=120°$. Prove that $OP=2AP$.

In the figure, find $PO\text{'}$, if $PQ=12 \mathrm{cm}$ and $O\text{'}R=5 \mathrm{cm}$.

In the figure, $OD$ is perpendicular to the chord $AB$ of a circle whose centre is $O$. If $BC$ is a diameter, show that $CA=2OD$.

A circle touches all the four sides of quad. $ABCD$. Prove that the angle subtended at the centre of the circle by the opposite sides are supplementary.

Two tangents$TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$. Prove that $\angle PTQ=2\angle OPQ$.

$ABC$ is a right triangle, right angled at $B$. A circle is inscribed in it. The lengths of the two sides containing the right angle are $6 \mathrm{cm}$ and $8 \mathrm{cm}$. Find the radius of the incircle.