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]