From a point P outside a circle two secants are drawn. The first meets the circle at A and then at B, with PA = 4 cm and PB = 15 cm. The second meets the circle at C and then at D, with PC = 5 cm. What is the length of PD?

Question

Accepted Answer

12 cm. For two secants from the same external point, PA × PB = PC × PD. So 4 × 15 = 5 × PD, giving 60 = 5 PD and PD = 12 cm. The value 7 cm is the chord CD = PD − PC, not the full secant length asked for.

From a point P outside a circle two secants are drawn. The first meets the circle at A and then at B, with PA = 4 cm and PB = 15 cm. The second meets the circle at C and then at D, with PC = 5 cm. What is the length of PD?

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