Question

There is a circle with centre C at the origin and radius r cm. Two tangents are drawn from an external point D at a distance d cm from the centre. What are the angles between each tangent and the X-axis?
Statement A
A. The coordinates of D are given.
Statement B
B. The X-axis bisects one of the tangents.

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

Hint:

For problems involving tangents and angles, knowing the coordinates or symmetry can be used to find the required angles.

Answer 1

The Correct Option is C

From Statement A: The coordinates of D give the necessary information to calculate the angles formed by the tangents with the X-axis using the tangent formula.
From Statement B: If the X-axis bisects one of the tangents, it implies symmetry, but without knowing the coordinates of D, we cannot determine the exact angles.
Combining both statements allows us to determine the required angles because we have both the geometric setup and symmetry, so the Correct Answer is (3).