The tangents drawn at the ends of a diameter of a circle are:a)intersecting at a point inside the circleb)perpendicularc)intersecting at the centre of the circled)parallelCorrect answer is option 'D'. Can you explain this answer?

Question

The tangents drawn at the ends of a diameter of a circle are:&#8203;a)intersecting at a point inside the circleb)perpendicularc)intersecting at the centre of the circled)parallelCorrect answer is option 'D'. Can you explain this answer?

Answer

Here AB is a diameter of the circle with centre O, two tangents PQ and RS drawn at points A and B respectively.

Radius will be perpendicular to these tangents.

Thus, OA ⊥ RS and OB ⊥ PQ

∠OAR = ∠OAS = ∠OBP = ∠OBQ = 90degree

Therefore,

∠OAR = ∠OBQ (Alternate interior angles)

∠OAS = ∠OBP (Alternate interior angles)

Since alternate interior angles are equal, lines PQ and RS will be parallel.

Answer

Yaa they will be parallel to each other

Answer

If the tangents are drawn at the ends of a diameter of a circle, then they will be PARALLEL to each other...

Answer

The tangents drawn at the ends of a diameter of a circle are parallel. Let's understand why this is the correct answer.

Understanding Tangents and Diameter:
- A tangent is a line that touches a circle at exactly one point, called the point of tangency.
- The diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle.

Properties of Tangents:
1. A tangent to a circle is perpendicular to the radius drawn to the point of tangency.
2. If a line is drawn from the center of a circle to the point of tangency, it is perpendicular to the tangent line.

Explaining the Tangents Drawn at the Ends of a Diameter:
To understand why the tangents drawn at the ends of a diameter are parallel, let's consider the following scenario:

1. Draw a circle and a diameter within it.
2. Draw two tangents from the endpoints of the diameter to the circle.
3. Since the diameter passes through the center of the circle, the tangents will intersect the circle at two different points.
4. According to the properties of tangents mentioned above, the radius drawn to the point of tangency is perpendicular to the tangent line.
5. As the tangents are drawn from the endpoints of the diameter, the radius drawn to the point of tangency will be perpendicular to the diameter as well.
6. Since the tangents are perpendicular to the diameter, they are also perpendicular to each other.
7. Two lines that are perpendicular to the same line are parallel to each other.
8. Therefore, the tangents drawn at the ends of a diameter of a circle are parallel.

Conclusion:
The correct answer is option 'D', the tangents drawn at the ends of a diameter of a circle are parallel. This can be understood by considering the properties of tangents and the fact that the tangents are perpendicular to the diameter of the circle.

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