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A circles is inscribed in a ABC touching AB, BC and AC at P,Q

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A circles is inscribed in a $△ A BC$ touching $A B, BC$ and $A C$ at $P, Q$ and $R$ respectively. If $A B = 10 c m, A R = 7 c m$ and $CR = 5 c m$ ., find the length of $BC$

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Olivia Discussed

A circles is inscribed in a

△ A BC

touching

A B, BC

and

A C

P, Q

and

R

respectively. If

A B = 10 c m, A R = 7 c m

and

CR = 5 c m

., find the length of

BC

5 mins ago

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Text solutionVerified

Given, a circle inscribed in

△ A BC

, such that the circle touches the sides of the triangle.

Tangents drawn to a circle from an external point are equal.

∴ A P = A R = 7

CQ = CR = 5

Now,

BP = A B - A P = 10 - 7 = 3

∴ BP = BQ = 3

∴ BC = BQ + QC = 3 + 5 = 8

∴

the length of

BC

8

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Question Text	A circles is inscribed in a $△ A BC$ touching $A B, BC$ and $A C$ at $P, Q$ and $R$ respectively. If $A B = 10 c m, A R = 7 c m$ and $CR = 5 c m$ ., find the length of $BC$
Answer Type	Text solution:1
Upvotes	150