Chapter 10 – Circles

13. If an isosceles triangle ABC, in which AB = AC = 6 cm, is inscribed in a circle of radius 9 cm, find the area of the triangle. 13. If an isosceles triangle ABC find the area of the triangle. in which AB = AC = 6 cm is inscribed in a circle of [...]

12. The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA=110º , find ∠CBA [see Fig. 9.21]. 12. The tangent at a point C of a circle and a diameter AB when extended intersect at P. If ∠PCA=110º find ∠CBA [see Fig. 9.21]. July 5, [...]

11. In Fig. 9.20. O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB. 11. In Fig. 9.20. O is the centre [...]

10. In Fig. 9.19, the common tangent, AB and CD to two circles with centres O and O’ intersect at E. Prove that the points O, E, O’ are collinear. -e 10. In Fig. 9.19 AB and CD to two circles with centres O and O' intersect at E. Prove that the points O O' [...]

9. Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc. 9. Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc. July [...]

8. AB is a diameter and AC is a chord of a circle with centre O such that ∠BAC = 30°. The tangent at C intersects extended AB at a point D. Prove that BC = BD. 8. AB is a diameter and AC is a chord of a circle with centre O such that [...]

7. In Fig. 9.18, tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find the ∠RQS. 7. In Fig. 9.18 tangents PQ and PR are drawn to a circle such that ∠RPQ = 30°. A chord RS is drawn parallel [...]

6. In a right triangle ABC in which ∠B = 90°, a circle is drawn with AB as diameter intersecting the hypotenuse AC and P. Prove that the tangent to the circle at P bisects BC. 6. In a right triangle ABC in which ∠B = 90° a circle is drawn with AB as diameter [...]

5. Two circles with centres O and O’ of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O’P are tangents to the two circles. Find the length of the common chord PQ. 5. Two circles with centres O and O' of radii 3 cm and [...]

4. If AB is a chord of a circle with centre O, AOC is a diameter and AT is the tangent at A as shown in Fig. 9.17. Prove that ∠BAT = ∠ACB 4. If AB is a chord of a circle with centre O AOC is a diameter and AT is the tangent at [...]