Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.
(N/A) Let $PR$ be a chord of a circle. Tangents are drawn at the points $P$ and $R$. Let these tangents meet at a point $T$ outside the circle.
In $\triangle TPR$,$TP = TR$ (tangents drawn from an external point to a circle are equal in length).
Since $TP = TR$,the angles opposite to these sides are equal,i.e.,$\angle TPR = \angle TRP$.
These angles are the angles made by the tangents with the chord $PR$.
Hence,the tangents drawn at the ends of a chord of a circle make equal angles with the chord.
In $\triangle TPR$,$TP = TR$ (tangents drawn from an external point to a circle are equal in length).
Since $TP = TR$,the angles opposite to these sides are equal,i.e.,$\angle TPR = \angle TRP$.
These angles are the angles made by the tangents with the chord $PR$.
Hence,the tangents drawn at the ends of a chord of a circle make equal angles with the chord.
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