Question

Problem E2 Moving points B and C are on circle x² + y2 = 25. Let A be (2,0) and M be mid-point of BC. If BAC is a straight line, what is the locus of M?​

Answer 1

Explanation:

The perpendicular bisector of any chord is a diameter and therefore passes through the center of the given circle.

The triangle OMA is thus rectangle.

The locus of M is the circle of diameter OA with center (1,0) and radius 1.