Question

A circle circumscribes a square. What is the area of the square?
[I.] Radius of the circle is given.
[II.] Length of the tangent from a point 5 cm away from the centre of the circle is given.

• A. if the question can be answered with the help of any one statement alone but not by the other statement.
• B. if the question can be answered with the help of either of the statements taken individually.
• C. if the question can be answered with the help of both statements together.
• D. if the question cannot be answered even with the help of both statements together.

Hint:

Use Pythagoras Theorem for tangents and radius to find geometric quantities.

Answer 1

The Correct Option is B

Statement I: If radius \( r \) of the circle is known, then the diagonal of the square is \( 2r \). Since diagonal of square is \( s\sqrt{2} \), we get: \[ s = \frac{2r}{\sqrt{2}} = r\sqrt{2}, \quad \text{Area} = s^2 = 2r^2 \] Statement II: If tangent from point 5 cm away is given, and length \( t \) is known, then radius can be found using: \[ r^2 = 5^2 - t^2 \Rightarrow r = \sqrt{25 - t^2} \] Then proceed as in Statement I. So both statements independently are sufficient.