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 by any one of the statements alone, but cannot be answered by using the other statement alone.
• B. If the question can be answered by using either statement alone.
• C. If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. If the question cannot be answered even by using both the statements together.

Answer 1

The correct option is B If the question can be answered by using either statement alone.


Statement (I) itself is sufficient to answer the question.
If we know the radius of the circle, we can find out the length of the diagonal of the square (which will be the diameter) and if we know the diagonal of a square we can find the length of its sides and hence the area. Again the second statement in itself can answer the question. As from the data that is given, we can find the radius of the circle and hence the area of the square (as given before). This can be explained by the diagram given. Since the tangent makes a right angle with the radius at the circumference, the triangle is a right-angled triangle. Hence, $A^2=5^2+r^2.$ Hence, knowing the value of A, we can find out r. Hence, both statements in itself can answer the question.