CDS 2025 · PYQ · Circles / Quadrilateral Area · medium
Two circles M (radius 8 cm) and N (radius 16 cm) touch externally. If U, V are the centres of the circles M and N respectively, then what is the area of the quadrilateral formed by the points P, Q, V and U?
A.192√2 square cm✓ Correct
B.192 square cm
C.96√2 square cm
D.96 square cm
Explanation
PUVQ is a trapezium with UP ⊥ PQ and VQ ⊥ PQ (radii perpendicular to tangent). UP = 8, VQ = 16, PQ = 16√2. Area of trapezium = (1/2)(UP + VQ) × PQ = (1/2)(8 + 16)(16√2) = (1/2)(24)(16√2) = 192√2 sq cm.
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