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Mathematics

In the figure, AB is common chord of the two circles. If AC and AD are diameters; prove that D, B and C are in a straight line. O1 and O2 are the centers of two circles.

In the figure, AB is common chord of the two circles. If AC and AD are diameters; prove that D, B and C are in a straight line. O1 and O2 are the centers of two circles. Circles, Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

We know that,

Angle in a semi-circle is a right angle.

∴ ∠DBA = ∠CBA = 90°

Adding both we get,

⇒ ∠DBA + ∠CBA = 180°

Hence proved that, D, B and C form a straight line.

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