Question

The locus of the midpoint of a line segment that is drawn from a given external point P to a given circle with centre O (where O is origin) and radius r, is 

(A) A straight line perpendicular to PO 

(B) A circle with centre P and radius r 

(C) A circle with centre P and radius 2r 

(D) A circle with centre at the midpoint PO and radius r/2

Answer 1

Correct option (D) A circle with centre at the midpoint PO and radius r/2

Explanation:

Equation of circle is x² + y² = r² Let P ≡ (a, b)

Let the midpoint of a point (h, k) on circle & P(a, b) be M(x, y)