CBSE Class 10CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

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

Login
Create free account


      Forgot password?

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?

Video TutorialsVIEW ALL [1]

Solution for question: Prove that the tangents at the extremities of any chord make equal angles with the chord. concept: Circles Examples and Solutions. For the course CBSE
S
View in app×