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

As we know that tangents drawn from an external point to a circle are equal ,

In the Given image we have,

AP = AR = 7 cm ….[1]

[tangents from point A]

CR = QC = 5 cm ….[2]

[tangents from point C]

BQ = PB …[3]

[tangents from point B]

Now,

AB = 10 cm [Given]

AP + PB = 10 cm

7 + PB = 10 [From 1]

PB = 3 cm

BQ = 3 cm …..[4]

[From 3]

BC = BQ + QC = 5 + 3 = 8 cm [ From 2 and 4]

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