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A circle is inscribed in a DeltaABC touc...

A circle is inscribed in a `DeltaABC` touching AB, BC and AC at P, Q and R respectively. If AB = 10 cm, AR = 7 cm and CR = 5 cm, then find the length of BC.

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We know that the lengths of tangents drawn from an external point to a circle are equal.
`:. AR=AQ=7cm`.
`BR=(AB-AR)=(10-7)cm=3cm`
`:.BP=BR=3cm`
`CP=CQ=5cm`
`:.BC=(BP+CP)=(3+5)cm=8cm`
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