31. AD is perpendicular to the internal bisector of ∠ABC of ΔABC. DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 12 cm, then the length of AE (in cm.) is
32. In the given figure, ABCD is a square whose side is 4 cm. P is a point on the side AD. What is the minimum value (in cm) of BP + CP?
33. Select the correct option with respect to the given statement.
Two tangents are drawn at the end of the diameter of a circle.
Two tangents are drawn at the end of the diameter of a circle.
34. Two circles touch each other externally at T. RS is a direct common tangent to the two circles touching the circles at P and Q. ∠TPQ = 42°. ∠PQT (in degrees) is:
35. In ΔABC, ∠ABC = 6∠ACB and ∠BAC = 5∠ACB. If AB = 7 cm and AC = 25 cm, then the length of BC is equal to:
36. In a triangle ABC, AB = 6√3 cm, AC = 12 cm and BC = 6 cm. Then measure of ∠B is equal to:
37. ABCD is a trapezium in which AB || DC and its diagonals intersect at P. If AP = (3x - 1) cm. PC = (5x - 3) cm. BP = (2x + 1) cm and PD = (6x - 5) cm, then the length of DB is:
38. In ΔABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 12 cm, CB = 8 cm, then CD is equal to:
39. A circle is inscribed in a quadrilateral ABCD touching AB, BC, CD and AD at the points P, Q, R and S, respectively, and ∠B = 90°. If AD = 24 cm, AB = 27 cm and DR = 6 cm, then what is the circumference of the circle?
40. In a circle, O is the centre of the circle. Chords AB and CD intersect at P. If ∠AOD = 32° and ∠COB = 26°, then the measure of ∠APD lies between:
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