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Question

Prove that in any circle, the tangents at two points make equal angles with the chord joining the points of contact.


Solution

Given: A circle with centre O

PA and PB are tangents to the circle through a point P and AB is the chord.

We know that lengths of tangents drawn from a point outside the circle are equal.

PA = PB

In ΔPAB, PA = PB 

We know that angles opposite to equal sides are equal in measure.

∴ ∠PBA = PAB

Thus, in a circle, the tangents at two points make equal angles with the chord joining the points of contact. 


Mathematics
Mathematics Part II
Standard X

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