The number of circles that can pass through two fixed points is:
Infinity
Fix two distinct points, say A and B. Any circle passing through both must have its centre at equal distance from A and B.
The complete set of points that are equidistant from A and B is the perpendicular bisector of the segment AB.
So every possible centre lies somewhere on this perpendicular bisector line.
Each point chosen on the bisector, taken as centre with radius equal to its distance to A (which equals its distance to B), produces a distinct circle through A and B.
Because a line contains infinitely many points, there are infinitely many valid centres and hence infinitely many circles.
Key concept: two points fix only the perpendicular bisector as the locus of centres; a unique circle needs a third non-collinear point.
Hence the number of circles is Infinity.
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An equilateral triangle ABC and a scalene triangle DBC are inscribed in a circle on same side of the arc. what is ∠BDC equal to?
In a circle with centre O, an arc ABC subtends an angle of 132° at the center of the circle. Chord AB is produced to point P. Then ∠CBP is equal to∶
