In the given figure, ΔABC is circumscribed. The circle touches the sides AB, BC and CA at P, Q, R respectively. If AP = 5 cm, BP = 7 cm, AC = 14 cm and BC = x cm, find the value of x.
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Question

In the given figure, ΔABC is circumscribed. The circle touches the sides AB, BC and CA at P, Q, R respectively. If AP = 5 cm, BP = 7 cm, AC = 14 cm and BC = x cm, find the value of x.

KnowledgeBoat · Accepted Answer

We know that,

Tangents from an exterior point to a circle are equal in length.

From A,

⇒ AP = AR = 5 cm

From figure,

⇒ AC = AR + RC

⇒ 14 = 5 + RC

⇒ RC = 14 - 5 = 9 cm

From B,

BP = BQ = 7 cm

From C,

CQ = CR = 9 cm

From figure,

⇒ BC = BQ + QC = 7 + 9 = 16 cm

⇒ x = 16 cm.

Hence, x = 16 cm.

Mathematics

In the given figure, ΔABC is circumscribed. The circle touches the sides AB, BC and CA at P, Q, R respectively. If AP = 5 cm, BP = 7 cm, AC = 14 cm and BC = x cm, find the value of x.

Circles

Answer

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