Two equal circles with centers A and B intersect at points P and Q, such that the center of each circle lies on the circumference of the other circle. The distance between centers of both the circles is 1 unit. What is the area of the rhombus APBQ (in sq. units)?
Explanation:
In ΔAPB, AP = AB = PB = 1
∴ ΔAPB is an equilateral triangle with side 1.
Similarly, ΔAQB is also an equilateral triangle with side 1.
∴ Area of the rhombus APBQ = A(ΔAPB) + A(ΔAQB)
= 34×12+34×12
∴ Area of a rhombus APBQ = 32 square units
Hence, option (a).
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