Question 89
Let $\triangle ABC$ be a triangle, let $M_A$ be the midpoint of the side $BC$, and let $P_A$ be the orthogonal projection of $A$ on the line $BC$; similarly, define $M_B, P_B$ and $M_C, P_C$. The lines $M_B M_C$ and $P_B P_C$ meet at $S_A$, and the tangent of the circle $ABC$ at $A$ meets the line $BC$ at $T_A$; similarly, define $S_B, T_B$ and $S_C, T_C$. Show that the perpendiculars through $A, B, C$ to the lines $S_A T_A, S_B T_B, S_C T_C$, respectively, are concurrent.
Flavian Georgescu
Flavian Georgescu