幾何與角

In the figure, $E$ and $F$ are the mid-points of $AB$ and $AC$ respectively. $G$ and $H$ divide $DB$ and $DC$ respectively in the ratio $1:3$. If $EF=12$, find $GH$.

In the figure, $ABC$ and $CDE$ are equilateral triangles. Find $\angle ADE$.

In the figure, $\text{arc }AB:\text{arc }BC:\text{arc }CD:\text{arc }DE:\text{arc }EA=1:2:3:4:5$. Find $\theta$.

In the figure, $M$ is the mid-point of $BC$ and $AD=2DB$. $AM$ and $CD$ intersect at $K$. Find $\dfrac{\text{area of }\triangle ADK}{\text{area of }\triangle AKC}$.

In the figure, which of the pairs of triangles must be congruent?

In the figure, $TQ$ is the tangent to the circle at $A$. If arc $AC$ = arc $BC$ and $\angle PAQ=48^\circ$, then $\angle QAC=$

In the figure, $AC\parallel DE$, $FG\parallel BC$ and $AD:DF:FB=1:2:3$. If $BE=10$, find $FG$.

In the figure, $ABCDE$ is a regular pentagon. Find $\angle AFD$.

In the figure, $AB$ is a diameter and $\angle BAC=30^\circ$. If the area of $\triangle ABC$ is $\sqrt{3}$, then the radius of the circle is

In the figure, $AC=CD$, $\angle ABC=30^\circ$ and $\angle CED=120^\circ$. $\dfrac{AB}{DE}=$