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Prove that the diameter AB of …

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Prove that the diameter AB of a cirlce bisects all thise chords which are parallel to the tangents at the point A.

Posted by Sourish D Great 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given: A circle with centre O and AOB is diameter.
CAD is a tangent at A. Chord EF || tangent CAD

To prove: AB bisects any chord EF || CAD.
Proof: OA radius is perpendicular to tangent CAD.
{tex}\therefore{/tex} {tex}\angle{/tex}1 = 90°
CAD || EF [Given]
{tex}\therefore{/tex} {tex}\angle{/tex}1 = {tex}\angle{/tex}2 = 90° [alternate interior angles]
Point M is on diameter which passes through centre O.
{tex}\because{/tex} Perpendicular drawn from centre to chord bisect the chord.
Hence, AB bisect any chord EF || CAD.

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