Chapter 10: Circles

Questions

1. Radius $7$, tangent length $24$: distance of external point.
2. Number of tangents from a point on the circle.
3. Two tangents from an external point are equal — true or false?
4. Radius $5$, external distance $13$: tangent length.
5. Angle between tangents from external point $= 60^\circ$. Central angle?
6. Two concentric circles $r = 5, r = 3$. Length of chord of larger tangent to smaller.
7. Draw tangents from a point $6$ cm from centre of circle of radius $3$.
8. In cyclic quadrilateral, opposite angles sum to?
9. Two circles of radii $r_1, r_2$ with centres $d$ apart, externally touching. Then $d = ?$
10. A quadrilateral $ABCD$ is drawn to circumscribe a circle. Prove $AB + CD = AD + BC$.

Extra Practice (Optional)

• Radius $8$, tangent length $15$: distance of point.
• Prove: tangent perpendicular to radius.
• Two tangents from external point subtend equal angles at centre.
• Common tangents of two circles $r_1, r_2$ externally touching.
• In $\triangle ABC$ inscribed in a circle with $\angle A = 60^\circ$, find arc $BC$.