The tangent at any point of the circle is _______to the radius through the point of contact.

Options

A. A)parallel
B. B)Intersecting
C. C)perpendicular
D. D)equal

Answer

To solve the question, "The tangent at any point of the circle is _______ to the radius through the point of contact," we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- A **tangent** to a circle is a straight line that touches the circle at exactly one point.
- A **radius** is a line segment from the center of the circle to any point on the circle.

2. **Draw the Circle**:
- Start by drawing a circle. Label the center of the circle as point O.

3. **Identify the Point of Contact**:
- Choose any point on the circumference of the circle. Label this point as A.

4. **Draw the Tangent**:
- From point A, draw a straight line that touches the circle at point A but does not cross it. Label this line as tangent AB.

5. **Draw the Radius**:
- Draw a line segment from the center O to the point A. This line segment OA is the radius of the circle.

6. **Analyze the Angles**:
- At the point of contact A, the tangent line AB and the radius OA form an angle. By the properties of circles, this angle is 90 degrees (i.e., they are perpendicular to each other).

7. **Conclusion**:
- Therefore, we conclude that the tangent at any point of the circle is **perpendicular** to the radius through the point of contact.

### Final Answer:
The tangent at any point of the circle is **perpendicular** to the radius through the point of contact.