# NCERT Mathematics Class 10 Exemplar Ch 9 Circles Part 6

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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.

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

Answer:

12. The tangent at a point C of a circle and a diameter AB when extended intersect at P. If , find CBA [see Fig. 9.21].

[Hint: Join C with centre O.]

Answer:

13. If an isosceles triangle ABC, in which , is inscribed in a circle of radius 9 cm, find the area of the triangle.

Answer:

14. A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the ΔABC.

Answer: