MathDB

Let

ABC

a triangle be given with

BC = a

CA = b

AB = c

(

a \neq b \neq c \neq a

). In plane (

ABC

) take the points

A'

B'

C'

such that: I. The pairs of points

A

and

A'

B

and

B'

C

and

C'

either all lie in one side either all lie in different sides under the lines

BC

CA

AB

respectively; II. Triangles

A'BC

B'CA

C'AB

are similar isosceles triangles. Find the value of angle

A'BC

as function of

a, b, c

such that lengths

AA', BB', CC'

are not sides of an triangle. (The word "triangle" must be understood in its ordinary meaning: its vertices are not collinear.)

Problem Statement