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2025 · Q56

Consider the following for the next two (02) items that follow: A circle M of radius 8 cm touches externally another circle N of radius 16 cm. Let P and Q be the points where the common tangent touches the circles M and N, respectively. 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?

Elementary MathematicsCircles
  1. A192√2 square cm
  2. B192 square cm
  3. C96√2 square cm
  4. D96 square cm

Explanation

The external tangent length is PQ = √(24² − (16−8)²) = √(576−64) = 16√2. PQUV is a trapezoid with parallel sides 8 and 16 and height 16√2, so area = (1/2)(8+16)(16√2) = 192√2 cm², option (a).