Question

Assertion (A): The area of the square inscribed in a circle of radius $$10\ \text{cm}$$ is $$200\ \text{cm}^{2}$$.

Reason (R): Diagonal of inscribed square = diameter of circle.

Options

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

Explanation:

Step 1 – Assertion: A is true. The diagonal of the square is the circle’s diameter, $$20\ \text{cm}$$. The area is $$\frac{1}{2}(20)^{2} = 200\ \text{cm}^{2}$$.

Step 2 – Reason: R is true. The diagonal joins two opposite vertices on the circle and is therefore a diameter.

Step 3 – Link: The reason gives the diagonal needed to calculate the square’s area, so it correctly explains the assertion.