Prove that the tangents drawn at

Question:

Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

Solution:

To prove ∠1 = ∠2, let PQ be a chord of the circle. Tangents are drawn at the points R and Q.

Let P be another point on the circle, then, join PQ and PR.

Since, at point Q, there is a tangent.

$\therefore$ $\angle 2=\angle P \quad$ [angles in alternate segments are equal]

Since, at point $R$, there is a tangent.

$\therefore$ $\angle 1=\angle P$ [angles in alternate segments are equal]

$\therefore$ $\angle 1=\angle 2=\angle P$ 

Hence proved.

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