51. In the given figure, PQRS is a quadrilateral. If QR = 18 cm and PS = 9 cm, then what is the area (in cm2) of quadrilateral PQRS?
52. 
In the given figure, if OQ = QR, then the value of m is:
In the given figure, if OQ = QR, then the value of m is:
53. Two circles are of radii 7 cm and 2 cm their centres being 13 cm apart. Then the length of direct common tangent to the circles between the points of contact is
54. The difference between the two perpendicular sides of a right-angled triangle is 17 cm and its area is 84 cm2. What is the perimeter (in cm) of the triangle?
55. The side BC of a triangle ABC is extended to the point D. If ∠ACD = 132° and ∠B = $$\frac{4}{7}$$∠A, then the measure of ∠A is equal to:
56. In the given figure, B and C are the centres of the two circles. ADE is the common tangent to the two circles. If the ratio of the radius of both the circles is 3 : 5 and AC = 40, then what is the value of DE?
57. In a circle with centre O, AB is a diameter and CD is a chord which is equal to the radius OC. AC and BD are extended in such a way that they intersect each other at a point P, exterior to the circle. The measure of ∠APB is
58. A circle touches the side PQ of a ΔAPQ at the point R and sides AP and AQ produced at the points B and C, respectively. If the perimeter of ΔAPQ = 30 cm, then the length of AB is:
59. In the given figure, AB = 30 cm and CD = 24 cm. What is the value (in cm) of MN?
60. In the given figure, if AD = 3, DE = 4, AB = 12, BF = 2, FG = 6, BC = 10, then the value of $$\frac{{\text{M}}}{{\text{N}}}$$ is: (Assume: M is the area of the quadrilateral FGDE and N is the area of the triangle ABC.)
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