Question

What is the angle between the tangent drawn at any point of a circle and the radius passing through the point of contact?

• A. \(30^\circ\)
• B. \(45^\circ\)
• C. \(60^\circ\)
• D. \(90^\circ\)

Hint:

This is one of the most important theorems in the study of circles. It's the basis for solving many geometry problems. Memorize it: Radius \(\perp\) Tangent at the point of contact.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question asks for a direct statement of a fundamental theorem related to tangents and radii of a circle.

Step 2: Detailed Explanation:
The theorem states that the tangent at any point on a circle is perpendicular to the radius that passes through that point of contact.
"Perpendicular" means that the angle formed between the two lines (the tangent and the radius) is \(90^\circ\).

Step 3: Final Answer:
Therefore, the angle between the tangent and the radius at the point of contact is \(90^\circ\). This corresponds to option (D).