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CAT 2025 Slot 3 · Quant · Circles · medium

Two chords AB and CD of a circle intersect at an interior point P. AP = 6 cm, PB = 8 cm and CP = 4 cm. Find the length of PD (in cm).

Numerical answer

Two chords AB and CD of a circle intersect at an interior point P. AP = 6 cm, PB = 8 cm and CP = 4 cm. Find the length of PD (in cm).
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Answer: 12

By the intersecting chords theorem, when two chords of a circle intersect inside the circle, the products of their segments are equal: AP×PB = CP×PD. Substituting, 6×8 = 4×PD, so 48 = 4×PD, giving PD = 12 cm.
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Original question written in the CAT 2025 Slot 3 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake