Embibe Experts Solutions for Chapter: Circles, Exercise 1: Rajasthan Board-2018

In fig. $AOB$ is the diameter of a circle and $C,D \text{and} E$ are three points situated on semi circle. Find the value of $\angle ACD+\angle BED$.

Prove that the opposite angles of cyclic quadrilateral are supplementary or sum is $180°$.

Prove that if a chord is drawn from a point of contact of the tangent of the circle then angle made by this chord with the tangent are equal to the respective alternate angles made by segments with this chord.

Find the length of the tangent of the circle with radius $5 \mathrm{cm}$ drawn from the point $13 \mathrm{cm}$ away from the centre of the circle.

In the given figure a quadrilateral $ABCD$ have $AB=AC=AD$, then prove that $\angle BAD=2(\angle BDC+\angle CBD)$.

A circle touches the side $BC$ of $∆ABC$ at point $P$ externally and touches other two sides $AB$ and $AC$ when produced at point $Q$ and $R$ respectively, then prove that $AQ=\frac{1}{2}(AB+BC+CA)$.

Prove that the angle formed by an arc on the centre of the circle is twice the angle formed at any point of remaining part of the circle.

Prove that an exterior angle formed by increasing side of a quadrilateral is equal to the interior opposite angle, then it is a cyclic quadrilateral.