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

Explanation

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.
`angleMAO=90^(@)`
[tangent at any point of a circle is perpendicular to the radius through the point of contact]
`angleCEO=angleMAO` [corresponding angles]
`:.angleCEO=90^(@)`
Thus, OE bisects CD, [perpendicular from centre of circle to the radius through the point of contact]
Similarly, the diameter AB bisects all. Chords which are parallel to the tangent at the point A.