Embibe Experts Solutions for Chapter: Tangents and Secants to a Circle, Exercise 1: Exercise

Prove that the angle between two tangents drawn from the same external point is supplementary to the angle subtended at the centre by the chord which is formed by joining the contact points of the tangents.

Draw a circle and two lines parallel to a given line such that one is tangent and the other, a secant to the circle.

What sort of a quadrilateral is formed by the tangents at the ends of two perpendicular diameters of a circle?

Calculate the area of the designed region in figure given below,common between the two quadrants of the circles of radius$10 \mathrm{cm}$ each(use $\pi =3.14$).
 

The length of the minute hand of a clock is $14 \mathrm{cm}$. Find the area swept by the minute hand in $10 \mathrm{minutes}$. Take $\mathrm{\pi }=\frac{22}{7}$

In figure, given below, $OACB$ is a quadrant of a circle with Centre $O$ and radius $3.5 \mathrm{cm}$. If $OD=2 \mathrm{cm}$. Find the area of the shaded region.(use $\mathrm{\pi }=\frac{22}{7}$)

Find the area of sector whose radius is $7 \mathrm{cm}$ with the angle $30°$. Take $\mathrm{\pi }=\frac{22}{7}$

In the given figure, $OABC$ is a square of side $7 \mathrm{cm}$. If $COPB$ is a quadrant of a circle with centre $C$. If the area of the shaded region is $\mathrm{k} {\mathrm{cm}}^2$ then, write the value of $\mathrm{k}$.