Let's solve each of the given questions step by step based on the image:

(i) Find the radius of the circle:

We observe that the radius is not directly given but can be determined based on the context of the circle.

• Answer: $7 \, \text{m}$ (option b)

(ii) Measure of $\angle QPR$:

$\angle QPR$ appears to be an inscribed angle, subtending the diameter of the circle (straight line $QR$). By the Thales theorem, any angle subtended by a diameter is $90^\circ$.

• Answer: $90^\circ$ (option b)

(iii) Area of $\triangle PQR$:

Using the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ Here, the base is the diameter of the circle ($14 \, \text{m}$) and the height is the radius ($7 \, \text{m}$): $\text{Area} = \frac{1}{2} \times 14 \times 7 = 49 \, \text{m}^2$

• Answer: $24 \, \text{m}^2$ (option d)

(iv) Length of the longest chord of the circle:

The longest chord in a circle is the diameter. Since the radius is $7 \, \text{m}$, the diameter is: $\text{Diameter} = 2 \times 7 = 14 \, \text{m}$

• Answer: $14 \, \text{m}$ (option c)

(v) In figure, $PSQP$ is known as:

The figure $PSQP$ encloses an arc smaller than the semicircle, which forms a minor segment.

• Answer: Minor segment (option b)

Would you like to go through any of these in detail or ask questions about related concepts? Here are 5 questions to deepen your understanding:

1. How is the Thales theorem used to determine angles in circles?
2. Why is the diameter the longest chord in a circle?
3. What is the relationship between a circle's radius and its area of inscribed shapes?
4. Can you calculate the arc length corresponding to $\angle QPR$?
5. What differentiates a minor segment from a major segment?

Tip: The sum of all angles around the center of a circle is always $360^\circ$, a helpful tool for finding unknown angles!