31. Two circles of radius 13 cm and 15 cm intersect each other at points A and B. If the length of the common chord is 24 cm, then what is the distance between their centres?
32. In the given figure, SX is tangent. SX = OX = OR. If QX = 3 cm and PQ = 9 cm. Then what is the value (in cm) of OS ?
33. In a circle of radius 10 cm, with centre O, PQ and PR are two chords each of length 12 cm. PO intersects chord QR at the points S. The length of OS is:
34. ABCD is a quadrilateral such that ∠D = 90°. A circle with centre O touches the sides AB, BC, CD and DA at P, Q, R and S, respectively. If BC = 40 cm, BP = 28 cm and CD = 25 cm, then what is the radius of the circle?
35. In ΔABC, Perimeter of ΔABD = Perimeter of ΔBCD and AB = 60 cm, BC = 80 cm and AC = 100 cm. Then find BD.
36. The lengths of the two sides forming the right angle of a right-angled triangle are 21 cm and 20 cm. What is the radius of the circle circumscribing the triangle?
37. Two sides of a triangle are of length 3 cm and 8 cm. If the length of the third side is '$$x$$' cm, then:
38. In a triangle PQR, ∠PQR = 90°, PQ = 10 cm and PR = 26 cm, then what is the value (in cm) of inradius of incircle?
39. The circles of same radius 13 cm intersect each other at A and B. If AB = 10 cm, then the distance between their centres
40. In ΔABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm, CD = 8 cm, then CB (in cm) = ?
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