Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.
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, the diameter AB bisects all.
Chords which are parallel to the tangent at the point A.
Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
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