Monthly Archives: July 2021

In acute $\triangle{ABC}$, $D$ and $E$ are on $AB$ and $AC$ respectively, and $CD\perp AB$, $BE\perp AC$. Draw perpendicular lines from $B$ and $C$ toward line $DE$, intersecting $DE$ at $F$ and $G$ respectively. Show that $DF=EG$.

Let $ABCD$ be a quadrilateral such that $AB = AC, \angle BAC = 20^\circ, AD = CD,$ and $\angle ADC = 100^\circ$ . Show that $AB = BC + CD$.