Tangents drawn at the end points of a diameter are

Options

A. Perpendicular
B. Parallel
C. Intersecting
D. None of these

Answer

To solve the question "Tangents drawn at the end points of a diameter are?", we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Diameter and Tangents**:
- Let AB be the diameter of the circle, where A and B are the endpoints of the diameter.
- Let CD and YZ be the tangents drawn at points A and B respectively.

2. **Understand the Properties of the Circle**:
- The radius OA is equal to OB since both are radii of the same circle.
- According to the theorem, the radius is perpendicular to the tangent at the point of contact. Therefore, OA is perpendicular to CD and OB is perpendicular to YZ.

3. **Establish the Angles**:
- Since OA is perpendicular to CD, we can say that angle OAC = 90 degrees.
- Similarly, since OB is perpendicular to YZ, angle OBY = 90 degrees.

4. **Sum the Angles**:
- Now, we can add the two angles:
\[ \text{Angle OAC} + \text{Angle OBY} = 90^\circ + 90^\circ = 180^\circ \]

5. **Apply the Transversal Line Concept**:
- The line AB (the diameter) acts as a transversal line intersecting the two lines CD and YZ.
- According to the properties of parallel lines, if the sum of the internal angles formed by a transversal is 180 degrees, then the two lines must be parallel.

6. **Conclusion**:
- Therefore, we conclude that the tangents CD and YZ drawn at the endpoints of the diameter AB are parallel.

### Final Answer:
The tangents drawn at the end points of a diameter are parallel.

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