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# In the Figure, Ab is Common Chord of the Two Circle. If Ac and Ad Are Diameters; Prove that D, B and C Are in a Straight Line. O1 and O2 Are the Centres of Two Circles. - ICSE Class 10 - Mathematics

ConceptChord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord

#### Question

In the figure, AB is common chord of the two circle. If AC and AD are diameters; prove that D,
B and C are in a straight line. O1 and O2 are the centres of two circles. #### Solution ∠DBA = 90° and ∠CBA = 90°

(Angles in a semicircle is a right angle) Adding both we get,
∠DBC = 180°
∴ D, B and C form a straight line.

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Solution In the Figure, Ab is Common Chord of the Two Circle. If Ac and Ad Are Diameters; Prove that D, B and C Are in a Straight Line. O1 and O2 Are the Centres of Two Circles. Concept: Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord.
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