Question 150
Let the sides of a scalene triangle $\triangle ABC$ be $AB = c$, $BC = a$, $CA = b$, $D$, $E$, $F$ be points on $BC$, $CA$, $AB$, such that $AD$, $BE$, $CF$ are angle bisectors of the triangle, respectively. Assume that $DE = DF$. Prove that
$$
(1) \frac{a}{b+c} = \frac{b}{c+a} + \frac{c}{a+b};
$$
$$
(2) \angle BAC \gt 90^{\circ}.
$$
$$
(1) \frac{a}{b+c} = \frac{b}{c+a} + \frac{c}{a+b};
$$
$$
(2) \angle BAC \gt 90^{\circ}.
$$