Chapter 9: Circles

Questions

1. Radius $13$; chord at $5$ from centre — chord length.
2. $60^\circ$ at centre — angle at circumference?
3. Angle in semicircle?
4. Number of tangents from an outside point?
5. Are all radii equal?
6. Prove: perpendicular from centre bisects chord.
7. Cyclic quad: $\angle A = 80^\circ, \angle B = 90^\circ$. Find $\angle C, \angle D$.
8. Two equal chords in a circle — where do they lie relative to centre?
9. Chord of length $10$ cm in circle $r = 13$. Distance from centre.
10. Angle subtended by a diameter at any point on the circle.

Extra Practice (Optional)

• Chord length $= 8$ in a circle radius $5$: distance from centre.
• Angle subtended by an arc at centre is $120^\circ$: inscribed angle?
• In cyclic $ABCD$: $\angle A + \angle C = ?$
• Prove angles in same segment are equal.
• Given a chord, construct its perpendicular bisector.