Question

In the figure angles between chords and radius are same. Prove that the length of chords are equal.​

Answer 1

Answer:

Perpendiculars are drawn from the centre of the circle to the chords.

Consider ΔAOM, ΔCON;

OM = ON

OA = OC (radii)

∠AMO = ∠CNO = 90°

∠A = ∠C (given)

ΔAOM ≅ ΔCON (A.A.S)

In equal triangles, angle opposite to equal sides are equal.

AM = CN

½AB = ½CD

∴ AB = CD

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