幾何與角

In the figure, $x$, $y$ and $z$ are the exterior angles of $\triangle ABC$. If $x:y:z=4:5:6$, then $\angle BAC=$

In the figure, $CDEF$ is a sector of a circle which touches $AB$ at $E$. If $AB=25$ and $BC=15$, find the radius of the sector.

In the figure, $AD:DB=1:2$, $AE:EC=3:2$. Area of $\triangle BDE$ : Area of $\triangle ABC=$

In the figure, area of $\triangle ABC$ : area of square $BCDE=2:1$. Find $PQ:BC$.

In the figure, $ABCD$ is a semi-circle, $CDE$ and $BAE$ are straight lines. If $\angle CBD=30^\circ$ and $\angle DEA=22^\circ$, find $x$.

In the figure, $OABCD$ is a sector of a circle. If $\overset{\frown}{AB}=\overset{\frown}{BC}=\overset{\frown}{CD}$, then $x=$

In the figure, $AB\parallel DC$ and $\angle DAB=\angle DBC$. Which of the following is/are true?

I. $\dfrac{AB}{BD}=\dfrac{BD}{DC}$ II. $\dfrac{AB}{BD}=\dfrac{AD}{BC}$ III. $\dfrac{AD}{BD}=\dfrac{BD}{CD}$

In the figure, points $A$, $B$, $C$ and $D$ are concyclic. Find $x$.

In the figure, $BA\parallel DE$ and $AC=AD$. Find $\theta$.

In the figure, $AB$ is a diameter. Find $\angle ADC$.