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

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#### Solution

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.

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