Tamil Nadu Board Solutions for Chapter: Geometry, Exercise 11: Exercise 4.4

$\mathrm{PQ}$ is a tangent drawn from a point $\mathrm{P}$ to a circle with centre $\mathrm{O}$ and $\mathrm{OQR}$ is a diameter of the circle such that $\angle \mathrm{POR}=120°$. Find $\angle \mathrm{OPQ}$.

An artist has created a triangular stained-glass window and has one strip of small length left before completing the window. She needs to figure out the length of the left out portion based on the lengths of the other sides as shown in the figure. If the length of the remaining one strip is $k \mathrm{cm}$, then find the value of $k$.

Draw a tangent at any point $\mathrm{R}$ on the circle of radius $3.4 \mathrm{cm}$ and centre at $\mathrm{P}$. 

Draw a circle of radius $4.5 \mathrm{cm}$. Take a point on the circle. Draw the tangent at that point using the alternate tangent theorem.

Draw the two tangents from a point which is $10 \mathrm{cm}$ away from the centre of a circle of radius $5 \mathrm{cm}$. Also, measure the length of the tangents.

Take a point which is $11 \mathrm{cm}$ away from the centre of the circle of radius $4 \mathrm{cm}$ and draw the two tangents to the circle from that point. 

Draw the two tangents from a point which is $5 \mathrm{cm}$ away from the centre of the circle of diameter $6 \mathrm{cm}$. Also, measure the lengths of the tangents.

Draw a tangent to the circle from the point $\mathrm{P}$ having radius $3.6 \mathrm{cm}$, and centre at $\mathrm{O}$. Point $\mathrm{P}$ is at a distance $7.2 \mathrm{cm}$ from the centre.