Problem (1) Let $M$ be the midpoint of the line segment $AB$.       Connect $M$ to a point $P$ outside this line.       If $MP<MA$, which is $∠APB$ an acute or obtuse angle?       Furthermore, what if $MP>MA$? (2) Prove that the midpoint of the hypotenuse of a right…

Problem Let $D$ and $E$ be points on sides $BC$ and $CA$ respectively of a triangle $ABC$, such that $$BD=\frac{1}{2} DC \qquad and \qquad CE=EA.$$ Then $AD$ bisects $BE$. $$ $$ $$ $$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $\downarrow$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ $$ Solution Let $F$…