Two chords $AB,CD$ of a circle intersect externally at a point $P$. If $PB=7 \mathrm{cm}$, $AB=9 \mathrm{cm}$ and $PD=6 \mathrm{cm}$, find $CD$.

In the figure given below, chord $AB$ and diameter $CD$ of a circle with centre $O$ meet at $P$. $PT$ is tangent to the circle at $T$. If $AP=16 \mathrm{cm}, AB=12 \mathrm{cm}$ and $DP=2 \mathrm{cm}$, find the length of $PT$ and the radius of the circle.

In the figure given below, chord $AB$ and diameter $CD$ of a circle meet at $P$. If $AB=8 \mathrm{cm}, BP=6 \mathrm{cm}$ and $PD=4 \mathrm{cm}$, find the radius of the circle. Also find the length of the tangent drawn from $P$ to the circle.

In the adjoining figure, chord $AB$ and diameter $PQ$ of a circle with centre $O$ meet at $X$. If $BX=5 \mathrm{cm}, OX=10 \mathrm{cm}$ and the radius of the
circle is $6 \mathrm{cm}$, compute the length of $AB$. Also find the length of tangent drawn from $X$ to the circle.

In the figure given below, $\angle \mathrm{CBP}=40°,\angle \mathrm{CPB}=q°$ and $\angle \mathrm{DAB}=p°$. Obtain an equation connecting $p$ and $q$. If $AC$ and $BD$ meet at $Q$ so that $\angle \mathrm{AQD}=2q°$ and the points $C,P,B$ and $Q$ are concyclic, find the values of $p$ and $q$.

In the figure given below, $AC$ is a diameter of the circle with centre $O$. If $CD\Vert BE, \angle AOB=130°$ and $\angle ACE=20°$, find $\angle BEC$.

In the figure given below, $AC$ is a diameter of the circle with centre $O$. If $CD\Vert BE, \angle AOB=130°$ and $\angle ACE=20°$, find $\angle BCD$.

In the figure given below, $AC$ is a diameter of the circle with centre $O$. If $CD\Vert BE,\angle AOB=130°$ and $\angle \mathrm{ACE}=20°$, find  $\angle \mathrm{CED}$.

In the figure given below, chords $AB, BC$ and $CD$ of a circle with centre $O$ are equal. If $\angle BCD=120°$, find $\angle BDC$.