MathDB

In a triangle, a symmedian is a line through a vertex that is symmetric to the median with the respect to the internal bisector (all relative to the same vertex). In the triangle

ABC

, the median

m_a

meets

BC

A'

and the circumcircle again at

A_1

. The symmedian

s_a

meets

BC

M

and the circumcircle again at

A_2

. Given that the line

A_1A_2

contains the circumcenter

O

of the triangle, prove that:
(a)

\frac{AA'}{AM} = \frac{b^2+c^2}{2bc} ;

(b)

1+4b^2c^2 = a^2(b^2+c^2)

Problem Statement