Divide a line segment PQ in the ratio a : b (a, b are positive integers), draw a ray PX so that ∠QPX is an acute angle and then mark points on ray PX at equal distances such that minimum 8. 9. 10. A circle is inscribed in a ∆ABC having sides AB = 10 cm, BC = 12 cm and CA = 16 cm and circle touches the sides AB, BC and AC of triangle ABC at P, Q and R respectively. Find AP, BQ and CR. [3] Two circles of equal radius 6 cm such that the distance between their centres is 15 cm, find the length of transverse common tangent. [3] In the given figure, two circles C1 and C2 touch each other internally at Q with centres O and O′ respectively. If radii of bigger and smaller circles are 4 cm and 3 cm respectively and ACDB is the straight line of 2 15 cm, then find the lengths of OA and AC. [4] CA 2 CC1 P O′OQ D B Oisthecentreofacircleofradius6cm.Pisa point such that OP = 10 cm and OP intersects the circle at T and PC, PD are two tangents drawn to the circle. If AB is the tangent to the circle at T, find the length AB. [4] CA 6 cm number of these points is (1) Greaterofaandb (3) a+b–1 (2) a+b [1] (4) a+b+1