MathDB

Let

a

and

b

be two positive real numbers, and

AB

a segment of length

a

on a plane. Let

C,D

be two variable points on the plane such that

ABCD

is a non-degenerate convex quadrilateral with

BC=CD=b

and

DA=a

. It is easy to see that there is a circle tangent to all four sides of the quadrilateral

ABCD

. Find the precise locus of the point

I

Problem Statement