Question 18
Let $ABC$ an isosceles triangle in $A$, $D$ the foot of the height from $A$ and $M$ an inner point at $ADC$ such as $\widehat{AMB}$ is obtuse and $\widehat{DBM} + \widehat{DAM} = \widehat{MCB}$. the lines $(CM)$ and $(AD)$ intersect in $P$, and the lines $(BM)$ and $(AD)$ intersect in $Q$. Let $S$ a point of $[AB]$ and $R$ a point of $[AM)$ unsure $[AM]$ such as $\widehat{SQB} = \widehat{DPC}$ and $\widehat{MRQ} = 2\widehat{QAM}$. To show that $QRS$ is isosceles.