In the figure, AB is a common chord of the two circles. If AC and AD are diameters; prove that D, B, and C are in a straight line. $O_1$ and $O_2$ are the centers of two circles.
Exercise 17 (A) | Q 6 | Page 258
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Given: Two circles with centre $O_1$ and $O_2$ intersect each other at A and B. AC and AD are the diameters of the circles.
To Prove: D, B, C are in the same straight line.
Construction: Join AB.
Proof:
$AO_1C$ is diameter.
∠ABC = 90°. .......(Angle in a semi-circle)
Similarly, ∠ABD = 90°,
Adding, we get:
∠ABC + ∠ABD = 90° + 90° = 180°
DBC is a straight line. or D, B, C are in the same line.
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