MathDB

Given two circle

M

and

N

, we say that

M

bisects

N

if they intersect in two points and the common chord is a diameter of

N

. Consider two fixed non-concentric circles

C_1

and

C_2

. a) Show that there exists infinitely many circles

B

such that

B

bisects both

C_1

and

C_2

. b) Find the locus of the centres of such circles

B

Problem Statement