Q. 84.3( 15 Votes )

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.


Answer :

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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