Question

P is a point inside a circle centered at O which does not coincide with the point O. How many chords can be drawn with P as the mid-point?

Answer 1

We need to know how many lines are possible which passes through P and intersects the circle at equal distances from the point P.

Lets draw a circle

This problem is best and easily approachable from the point of symmetry.

Condition is satisfied only when chord $AB$ is drawn perpendicular to the radius going through the point P.This brings in symmetry and we get $AP=BP$ for any other chord going through P will destroy the symmetry about the line $OP,AP\ne BP.$