幾何與角

In the figure, $PA$ and $PC$ are tangents to the circle $ABC$. If $\angle P=48^\circ$, then $\angle ABC=$

In the figure, $EA$ and $EB$ are tangents to the circle $ABC$. If $EA\perp EB$ and $BD\perp AC$, find $\angle CBD$.

In the figure, if $CD=CF$, $CE=BE$ and $DA=DB$, then $\angle C=$

In the figure $AB$, $AC$ and $BC$ are three tangents touching the circle at $D$, $E$ and $F$ respectively. If $AC=24$, $BC=18$ and $\angle ACB=90^\circ$, find the radius of the circle.

In the figure, $\triangle PTQ$, $\triangle SQR$ and $\triangle RUT$ are equilateral triangles. Which of the following is/are true? I. $\triangle UPT\cong\triangle RQT$ II. $PU=QS$ III. $PQSU$ is a parallelogram

Referring to the figure, find $y$.

In the figure, $ABCDE$ is a regular pentagon and $ABYE$ is a rhombus. Find $\angle CAY$.

In the figure, $O$ is the centre of two concentric circles. $ADOEB$ and $CGFB$ are straight lines. Which of the following is/are true?

I. $AC /\!/ DG$ II. $BF=CG$ III. $A$, $E$, $F$ and $C$ are concyclic

In the figure, $TC$ is a tangent to the circle at $C$ and $AB /\!/ DC$. If $\angle BCT=48^\circ$, then $\theta=$

In the figure, $D$ and $E$ are points on $AB$ and $AC$ respectively such that $\angle ABC=\angle AED$, $AD=8$, $AE=5$ and $EC=15$. If the area of $\triangle ADE$ is 16, then the area of the quadrilateral $BCED$ is