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Question

# A, B, C, D are 4 non collinear points in a plane such that ∠ ACB=∠ ADB, then how many circle(s) can be drawn passing through all 4 points?

A

True

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B

False

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C
2
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D
3
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Solution

## The correct option is B False Let us draw the points A, B, C, D such that ∠ACB = ∠ADB. Now draw a circle through A, B, C. Let us assume that the circle does not pass through the point D but intersects the extension of line segment CD at D′. Since angles subtended by an arc in a segment are equal, ∠ ACB=∠A D′B. It is given that ∠ACB=∠ADB. Thus for the angles to be equal, D and D′ should coincide. Thus our assumption that the circle does not pass through D is false. Therefore a circle can be drawn through these 4 points.

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