Category Archives: Geometry

In $\triangle ABC$, $D$ is on line $\overline{BC}$ and $\overline{BD}=\overline{CD}$, $E$ is on line $\overline{AC}$ and $\overline{AE}=2\overline{CE}$. Find the value of $\dfrac{\overline{DF}}{\overline{AF}}$.

In the following figure, point $C$, $D$ and $E$ are the middle points of line segment $AB$, $AC$ and $BC$, with the length of line segment $AB$ as $4$. Additionally, 6 semi-circles are drawn with diameters as $AD$, $AC$, $AE$, $DB$, $CD$ and $EB$. Find … Continue reading →

In the figure below, $D$ is the middle point of line $\overline{AB}$, $E$ is the middle point of $\overline{BC}$. $\overline{AE}$ and $\overline{CD}$ intersect at $F$. What is the area ratio $\triangle DEF$ and $\triangle ABC$?