Question

Prove that if P is in the interior of a circle and there are three congruent segments from P to the circumference of the circle, then P is the center of the circle.

Please be detailed.

Answer 1

consider a point p in the interior of the circle.

congruent segments are those having equal length.

let these congruent segments are drawn from p.

the distance of these segments from point p is equal since the segments are of equal length.

let the segments be PA,PB,PC where PA=PB=PC

If three segments are equal in length from a point then the segment is said to be radius of the circle from where the 3 segments are joined.

the point of intersection of three segments that is point p is the centre where PA,PB,PC are radii of the circle.