ΔABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Prove that the base is bisected by the point of contact.
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Question

ΔABC is an isosceles triangle in which AB = AC, circumscribed about a circle. Prove that the base is bisected by the point of contact.

KnowledgeBoat · Accepted Answer

We know that,

Tangents from exterior point are equal in length.

We have,

AR = AP, BQ = BP and CQ = CR

Now, AB = AC

⇒ AP + PB = AR + RC

⇒ AR + PB = AR + RC [∵ AR = AP]

⇒ PB = RC

⇒ BQ = CQ.

It means BC is bisected at point Q.

Hence, proved that the base is bisected by the point of contact.

Mathematics