MathDB

Three straight lines

\ell_1

\ell_2

and

\ell_3

, forming a triangle, divide the plane into

7

parts. Each of the points

M_1

M_2

and

M_3

lies in one of the angles, vertical to some angle of the triangle. The distance from

M_1

to straight lines

\ell_1

\ell_2

and

\ell_3

are equal to

7,3

and

1

respectively The distance from

M_2

to the same lines are

4

1

and

3

respectively. For

M_3

these distances are

3

5

and

2

. What is the radius of the circle inscribed in the triangle?
[hide=second sentence in Russian]Каждая из точек М_1, М_2 и М_з лежит в одном из углов, вертикальном по отношению к какому-то углу треугольника.

Problem Statement