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Two circles, S₁ and S₂ , of radii 6 units and 3 units respectively, are tangent to each other externally. Let A C and B D be their direct common tangents with A and B on S₁ , and C and D on S₂ . Find the area of quadrilateral A B D C to the nearest integer.

Correct answer

68

Step-by-step solution

Refer to diagram, = 3 9 = 1 3 Let ar ( A P R)= then ar ( B Q S)= 4 Because A P R B Q S aligned & = 1 2 A P P R & = 1 2 6 2 2 2 3 =4 2 aligned Area of A B D C=2 [ 1 2 72 (3+6)- + 4 ]=48 2

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