In the following figure, a tangent segment PA touching a circle in A and a secant PBC is shown. If AP = 15, BP = 10, find BC.

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#### Solution

PA is a tangent segment and PBC is the secant.

`therefore PB xx PC=PA^2` ........(Relationship to Tangent-Secant Theorem)

`therefore 10xxPC=15^2`

`PC=225/10=22.5`

`Now , PB+BC=PC`

`therefore 10+BC=22.5`

`therefore BC=22.5-10= 12.5`

Concept: Tangent - Secant Theorem

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