2017 · Q64
The diagonals of a cyclic quadrilateral ABCD intersect at P and the area of the triangle APB is 24 square cm. If AB = 8 cm and CD = 5 cm,then what is the area of the triangle CPD ?
Elementary MathematicsQuadrilaterals and Polygons
- A24 square cm
- B15 square cm
- C12.5 square cm
- D9.375 square cm
Explanation
In a cyclic quadrilateral, ∠PAB = ∠PDC and ∠PBA = ∠PCD (angles subtended by the same arcs), so △APB ∼ △DPC with linear ratio 8:5. Areas scale as 64:25, so area of CPD = 24×25/64 = 9.375. Hence option (D) 9.375 square cm.