In the adjoining figure, P is a point of intersection of two circles with centres C and D. If the straight line APB is parallel to CD, prove that AB = 2CD.
Circles
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Question

In the adjoining figure, P is a point of intersection of two circles with centres C and D. If the straight line APB is parallel to CD, prove that AB = 2CD.

KnowledgeBoat · Accepted Answer

From C draw CL perpendicular to AB and from D drawn DM perpendicular to AB. From figure, LCDM is a rectangle. ∴ ML = CD (Opposite sides of rectangle are equal). Since, the perpendicular to a chord from the centre of the circle bisects the chord, LP = AP and MP = PB From figure, LM = LP + PM Hence, proved that AB = 2CD.

Mathematics

In the adjoining figure, P is a point of intersection of two circles with centres C and D. If the straight line APB is parallel to CD, prove that AB = 2CD.

Circles

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