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Solution - Prove that the tangents at the extremities of any chord make equal angles with the chord. - CBSE Class 10 - Mathematics

ConceptCircles Examples and Solutions

Question

Prove that the tangents at the extremities of any chord make equal angles with the chord.

Solution

Let AB be a chord of a circle with centre O, and let AP and BP be the tangents at A and B respectively.

Suppose the tangents meet at P. Join OP. Suppose OP meets AB at C. We have to prove that ∠PAC = ∠PBC In triangles PCA and PCB, we have

PA = PB

[∵ Tangents from an external point are equal]

∠APC = ∠BPC

[∵PA and PB are equally inclined to OP] and, PC = PC [Common]

So, by SAS – criterion of congruence, we have

∆PAC ≅ ∆PBC

⇒ ∠PAC = ∠PBC

Is there an error in this question or solution?

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Reference Material

Solution for question: Prove that the tangents at the extremities of any chord make equal angles with the chord. concept: null - Circles Examples and Solutions. For the course CBSE
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