The sum of the interior angles of a regular polygon is $40$ times the exterior angle. Find the number of sides of the polygon.

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In the question find $\angle \mathrm{BAO}$.

Two circles having equal radius intersect each other at $\mathrm{A}$and $\mathrm{B}$as shown in the diagram below. The diameters $\mathrm{AC}$and $\mathrm{AD}$ intersect at $\mathrm{A}$. If $\mathrm{C}, \mathrm{B}, \mathrm{D}$ are collinear and $\angle \mathrm{ACB} = 30°$, then answer the following question

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Find $\angle \mathrm{CAD} =\mathrm{\_\_\_\_\_}$.

Two circles having equal radius intersect each other at $\mathrm{A}$and $\mathrm{B}$as shown in the diagram below. The diameters $\mathrm{AC}$and $\mathrm{AD}$ intersect at $\mathrm{A}$. If $\mathrm{C}, \mathrm{B}, \mathrm{D}$ are collinear and $\angle \mathrm{ACB} = 30°$, then answer the following question 

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If $\mathrm{BC} = 2 \mathrm{cm}$, then $\mathrm{AD} (\mathrm{in} \mathrm{cm})$

In the diagram $\mathrm{O}$O is the center of the circle. $\mathrm{PS}$ is the tangent of the circle at $\mathrm{S}$. $\angle \mathrm{OSQ}$$= 50°$. Find $\angle \mathrm{SPR}.$

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In the given diagram $\mathrm{ABCD}$is a trapezium. If $\mathrm{AB} = 4 \mathrm{cm}, \mathrm{CD} = 6 \mathrm{cm} \mathrm{and} \mathrm{OB} = 5 \mathrm{cm}, \mathrm{then} \mathrm{BD} =\mathrm{\_\_\_\_\_cm}.$

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