NCERT Solutions for Chapter: Circles, Exercise 1: Exercise

Below is 3D sketch of an arch bridge having span of $15 \mathrm{m}$ for each arch. The distance from the floor to the topmost most point of the arch is $4 \mathrm{m}$. 

Estimate the radius of curvature of the arch.

In the below given figure, $O$ is the centre and $AOE$ is the diameter of the semicircle. If $AB=BC$ and $\angle OEC=50°$. Find $\angle AOB$

Prove that $OB$ is parallel to $EC$

In the given figure, the points $M, R, N, P, S$ and $Q$ are concyclic. Find $\angle PQR+\angle OPR+\angle NMS+\angle OSN$, if $O$ is the centre of the circle.

Point $O$ is the centre of the circle.

If $BC= CD= DE$, then find $\angle ABE$.

In the figure below $∆ABC$ is an equilateral triangle. Bisector of $\angle B$ intersects circumcircle of $∆ABC$ in point $P.$ Prove that, $CQ=CA$

$PQ$ and $RQ$ are chords of a circle equidistant from the centre. Prove that the diameter passing through $Q$ bisect $\angle PQR$ and $\angle PSR$.

In the adjoining figure, $O$ is the centre of the circle. If chords $AC\text{ and }BD$ intersect at right angles at $E$ and $\angle OAB=35°.$ Calculate $\angle EBC.$

In the given figure, $OA$ and $OB$ are respectively perpendiculars to chords $CD$ and $EF$ of a circle whose centre is $O$. If $OA=OB$, then