MathDB

All sides of triangle

ABC

are different. On rays

B A

and

C A

the segments

B K

and

CM

are laid out, equal to side

BC

. Let us denote by

x

the length of the segment

KM

. In the same way, by plotting the side

AC

on the rays

AB

and

CB

from

A

and

C

, we obtain a segment of length

y

, and by plotting the side AB on the rays

AC

and

BC

, we obtain a segment of length

z

. a) Prove that a triangle can be formed from the segments

x

y

and

z

, and this triangle is similar to triangle

ABC

. b) Find the radius of the circumcircle of a triangle with sides

x

y

and

z

, if the radii of the circumscribed and inscribed circles of triangle

ABC

are equal to

R

and

r

respectively.

Problem Statement