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A point O is at a distance of 10 cm from the centre of a circle of radius 6 cm. How many tangents can be drawn from point O to the circle?
- a)2
- b)1
- c)Infinite
- d)0
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A point O is at a distance of 10 cm from the centre of a circle of rad...
Only two tangents can be drawn from an external point.No tangent can be drawn which touches points inside the circle.
Most Upvoted Answer
A point O is at a distance of 10 cm from the centre of a circle of rad...
Here point O is exterior point and only 2 tangents can be drawn from exterior point to the cirlce
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Community Answer
A point O is at a distance of 10 cm from the centre of a circle of rad...
The correct answer is option 'A': 2.
Explanation:
To understand why there are two tangents that can be drawn from point O to the circle, let's analyze the given information step by step.
1. The circle has a radius of 6 cm.
2. Point O is at a distance of 10 cm from the center of the circle.
From the given information, we can observe the following:
- The distance between the center of the circle and point O is greater than the radius of the circle. This means point O is located outside the circle.
- When a point is located outside a circle, two tangents can be drawn from that point to the circle.
Now, let's visualize this situation:
1. Draw a circle with a radius of 6 cm.
2. Mark the center of the circle.
3. Draw a point O outside the circle at a distance of 10 cm from the center.
4. Connect point O to the center of the circle.
We can see that the line joining point O and the center of the circle is the radius of the circle. Since the distance between point O and the center of the circle is greater than the radius, point O lies outside the circle.
To find the tangents, we can draw lines from point O that are perpendicular to the radius. These lines will touch the circle at two different points, forming two tangents.
Hence, the correct answer is that two tangents can be drawn from point O to the circle.
Explanation:
To understand why there are two tangents that can be drawn from point O to the circle, let's analyze the given information step by step.
1. The circle has a radius of 6 cm.
2. Point O is at a distance of 10 cm from the center of the circle.
From the given information, we can observe the following:
- The distance between the center of the circle and point O is greater than the radius of the circle. This means point O is located outside the circle.
- When a point is located outside a circle, two tangents can be drawn from that point to the circle.
Now, let's visualize this situation:
1. Draw a circle with a radius of 6 cm.
2. Mark the center of the circle.
3. Draw a point O outside the circle at a distance of 10 cm from the center.
4. Connect point O to the center of the circle.
We can see that the line joining point O and the center of the circle is the radius of the circle. Since the distance between point O and the center of the circle is greater than the radius, point O lies outside the circle.
To find the tangents, we can draw lines from point O that are perpendicular to the radius. These lines will touch the circle at two different points, forming two tangents.
Hence, the correct answer is that two tangents can be drawn from point O to the circle.
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