Question

Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.

Answer 1

Given, AB is a diameter of the circle.

A tangent is drawn from point A.

Draw a chord CD parallel to the tangent MAN.

So, CD is a chord of the circle and OA is a radius of the circle.

∴ ∠MAO = 90°   ...[Tangent at any point of a circle is perpendicular to the radius through the point of contact]

⇒ ∠CEO = ∠MAO  ...[Corresponding angles]

∴ ∠CEO = 90°

Thus, OE bisects CD,  ...[Perpendicular from centre of circle to chord bisects the chord]

Similarly, diameter AB bisects all chords which are parallel to the tangent at the point A.