Which of the following statement is CORRECT about the tangents?

Options

A. The tangents drawn at the end of diameter of a circle are parallel to each other.
B. The line segment which joins the point of contact of two parallel tangents to the circle is the diameter of the circle.
C. Tangents drawn from the external point subtend equal angle at the centre.
D. All options are correct.

Answer

To determine which statement is correct about tangents, let's analyze each option step by step.

### Step 1: Analyze the first statement
**Statement A:** The tangents drawn at the endpoints of the diameter of a circle are parallel to each other.

- **Explanation:** When you draw a diameter of a circle, the endpoints of the diameter lie on the circle. If you draw tangents at these points, they will be parallel because the radius at these points is perpendicular to the tangent line. Therefore, this statement is **correct**.

### Step 2: Analyze the second statement
**Statement B:** The line segment which joins the points of contact of the two parallel tangents to the circle is the diameter of the circle.

- **Explanation:** If two tangents are drawn parallel to each other, the line segment connecting their points of contact does indeed form a line that is equal to the diameter of the circle. This is because the distance between the two points of contact is the same as the diameter of the circle. Thus, this statement is also **correct**.

### Step 3: Analyze the third statement
**Statement C:** Tangents drawn from an external point to a circle subtend equal angles at the center.

- **Explanation:** When two tangents are drawn from an external point to a circle, they form equal angles with the line segment connecting the external point to the center of the circle. This is a property of tangents and circles. Therefore, this statement is also **correct**.

### Conclusion
All three statements about tangents are correct.

### Final Answer:
All options are correct.