Mathematics
In the given figure, AC is a diameter of a circle, whose centre is O. A circle is described on AO as diameter. AE, a chord of the larger circle, intersects the smaller circle at B.
Prove that : AB = BE.
Circles
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Answer
Join OB.
From figure,
∠OBA = 90° [As angle in a semi-circle is a right angle]
∴ OB is perpendicular to AE.
We know that,
The perpendicular draw from the centre to a chord bisects the chord.
∴ AB = BE.
Hence, proved that AB = BE.
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