Question

Assertion (A): The difference between the areas of two segments of a circle of radius $$5\ \text{cm}$$, formed by a chord subtending an angle of $$90^{\circ}$$ at the centre, is $$\left(\frac{25}{2}\pi + 25\right)\ \text{cm}^{2}$$.

Reason (R): The area of a segment of a circle is less than the area of the corresponding sector.

विकल्प

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (А).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (А).

Explanation:

Step 1 – Assertion: A is true. The minor segment area is $$\left(\frac{25\pi}{4} - \frac{25}{2}\right)\ \text{cm}^{2}$$ and the major segment area is $$\left(\frac{75\pi}{4} + \frac{25}{2}\right)\ \text{cm}^{2}$$. Their difference is $$\left(\frac{25\pi}{2} + 25\right)\ \text{cm}^{2}$$.

Step 2 – Reason: R is true. A segment is the part of a sector remaining after a triangle is removed, so its area is less than that of the corresponding sector.

Step 3 – Link: This fact compares a segment with its corresponding sector, but does not explain the difference between the two segment areas.