Question

The angle made by the tangent at any point of the circle with the radius at the point of contact is:

• A. \( 0^\circ \)
• B. \( 45^\circ \)
• C. \( 60^\circ \)
• D. \( 90^\circ \)

Hint:

Remember, the tangent to a circle is always perpendicular to the radius at the point of contact. This is crucial in many geometric problems involving tangents.

Answer 1

The Correct Option is D

Step 1: Understanding the Tangent-Radius Relationship.
At the point where a tangent touches the circle, the radius drawn to the point of contact is always perpendicular to the tangent. This is a well-established property of tangents to a circle. 
Step 2: Applying the Perpendicularity Rule.
Since the radius at the point of contact forms a right angle with the tangent, the angle between the tangent and the radius is always \( 90^\circ \). 
Step 3: Conclusion.
Therefore, the angle made by the tangent at any point of the circle with the radius at the point of contact is \( 90^\circ \).