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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? 


  1. 1
  2. 2
  3. 0
  4. 3


Solution

The correct option is A 1

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 DB. 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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