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