Question

Prove that the tangents drawn at the end points of a chord of a circle

make equal angles with the chord​

Answer 1

Consider a circle with centre, O and the chord PQ.

Tangents PT and QT meet at T.

OPQ is an isosceles triangle so that <PQO = <QPO = x. say.

<TPO = <TQO = 90 deg as PT and QT are tangents.

<TPQ = <TQP = 90 - x being complementary to the equal angles of the isosceles triangle OPQ.

Hence the tangents drawn at the ends of a chord of a circle make equal angles with the chord. Proved.