幾何與角

In the figure, $ABCD$ is a cyclic quadrilateral. If $\angle DAB=110^\circ$ and $BC=BD$, find $\angle DAC$.

In the figure, $AB=AC$ and $AD=AE$. $\angle DAC=$

In the figure, $\angle ADE=\angle ACB$. Find $x$.

In the figure, $DE=DB$, $AC=13$ and $BC=5$. Area of $\triangle ADE$ : Area of $\triangle ACB=$

In the figure, $a+b+c+d+e+f=$

According to the figure, which of the following must be true ?

In the figure, $O$ is the centre of the circle. If $AC=3$ and $\angle BAC=\dfrac{\pi}{6}$, find the diameter $AB$.

In the figure, $PA$ is tangent to the circle at $A$, $\angle CAP=28^\circ$ and $BA=BC$. Find $x$.

In the figure, $O$ is the centre of the inscribed circle of $\triangle ABC$. If $\angle OAC=30^\circ$ and $\angle OCA=25^\circ$, find $\angle ABC$.

In the figure, $AB=AD$ and $BC=CD$. If $\angle BAD=80^\circ$ and $\angle ADC=65^\circ$, then $\angle BCD=$