Category Archives: Geometry

In $\triangle{ABC}$, $AM$ is the median on the side $BC$. Prove that $AB^2+AC^2=2(AM^2 + BM^2)$ For $\triangle{ABC}$, $O$ is an inner point, and $D$, $E$, $F$ are on $BC$, $CA$, $AB$ respectively, such that $OD\perp BC$, $OE\perp CA$, and $OF\perp … Continue reading →

As shown in the diagram below, in $\triangle{ABC}$, $\angle{B}\gt \angle{C}$, $AD$ is the bisector of the $\angle{BAC}$, $AE\perp BC$ at $E$. Prove that $\angle{DAE}=\dfrac{1}{2}(\angle{B}−\angle{C})$. 2. There are four points $A$, $B$, $C$, $D$ on the plane, such that any three … Continue reading →