MathDB

Given a circle

C

and a diameter

AB

in it, mark a point

P

AB

different from the ends. In one of the two arcs determined by

AB

choose the points

M

and

N

such that

\angle APM = 60 ^ \circ = \angle BPN

. The segments

MP

and

NP

are drawn to obtain three curvilinear triangles;

APM

MPN

and

NPB

(the sides of the curvilinear triangle

APM

are the segments

AP

and

PM

and the arc

AM

). In each curvilinear triangle a circle is inscribed, that is, a circle is built tangent to the three sides. Show that the sum of the radii of the three inscribed circles is less than or equal to the radius of

C

Problem Statement