Exercise

Find all the angles of the given cyclic quadrilateral $ABCD$ in the figure.

In the given figure, $ABCD$ is a cyclic quadrilateral where diagonals intersect at $P$ such that $\angle DBC = 40°$ and $\angle BAC = 60°$ find  $\angle CAD$ and $\angle BCD$.

In the given figure, $AB$ and $CD$ are the parallel chords of a circle with centre $O$. Such that $AB=8 \mathrm{cm}$ and $CD=6 \mathrm{cm}$. If $OM\perp AB$ and $OL\perp CD$ distance between $LM$ is $7 \mathrm{cm}$. If the radius of the circle is $k cm$ then find the value of $k$.

The arch of a bridge has dimensions as shown, where the arch measure $2 \mathrm{m}$ at its highest point and its width is $6 \mathrm{m}$. If is the radius of the circle that contains the arch is $k m$ then find the value of $k$.

In figure, $\angle ABC=120°$, where $A, B$ and $C$ are points on the circle with centre $O$. If the value of $\angle OAC$ is $k°$ then find the value of $k$. 

A school wants to conduct tree plantation programme. For this a teacher allotted a circle of radius $6 \mathrm{m}$ ground to ninth standard students for planting sapplings. Four students plant trees at the points $A, B, C$ and $D$ as shown in figure. Here $AB=8 \mathrm{m}, CD=10 \mathrm{m}$ and $AB\perp CD$. If another student places a flower pot at the point $P$, the intersection of $AB$ and $CD$, then find the distance from the centre to $P$.

In the given figure, $\angle POQ=100°$ and $\angle PQR=30°$, then find $\angle RPO=k°$ then find $k$.

In a parallelogram $ABCD, P$ and $Q$ are the points on line $DB$ such that $PD=BQ$ show that $APCQ$ is a parallelogram