In the given figure, two circles intersect at $A$ and $B$. The centre of the smaller circle is $O$ and it lies on the circumference of the larger circle. If $\angle APB=70°$, find $\angle ACB$.

In the given figure, two congruent circles with centres $O$ and $O$' intersect at $A$ and $B$. If $\angle A{O}^{\text{'}}B=50°$ then find $\angle APB$.

In the given figure, $ABCD$ is a cyclic quadrilateral in which $\angle BAD=75°, \angle ABD=58°$ and $\angle ADC=77°$, $AC$ and $BD$ intersect at $P$. Then, find $\angle DPC$.

In the given figure, if $\angle AOB=80°$ and $\angle ABC=30°$, then find $\angle CAO$.

In the given figure, $A$ is the centre of the circle. $ABCD$ is a parallelogram and $CDE$ is a straight line. Find $\angle BCD:\angle ABE$.

In the given figure, $AB$ is a diameter of the circle such that $\angle A=35°$ and $\angle Q=25°$, find $\angle PBR$.

In the given figure, $P$ and $Q$ are centres of two circles intersecting at $B$ and $C$ . $ACD$ is a straight line. Then, $\angle BQD=$

In the given figure, if $\text{'}O\text{'}$ is the circumcentre of $△ABC$ then find the value of $\angle OBC+\angle BAC$.

In the given figure, $AOC$ is a diameter of the circle and arc $AXB=\frac{1}{2}$ arc $BYC$. Find $\angle BOC$.