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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)1
- b)3
- c)Infinite
- d)2
Correct answer is option 'D'. 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...
Two tangents can be drawn to a circle from a point outside the circle.
No tangent line can be drawn through a point within a circle, since any such line must be a secant line.
No tangent line can be drawn through a point within a circle, since any such line must be a secant line.
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A point O is at a distance of 10 cm from the centre of a circle of rad...
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A point O is at a distance of 10 cm from the centre of a circle of rad...
Explanation:
When a line is drawn from a point outside a circle to the circle, it is called a tangent. The tangent line touches the circle at exactly one point.
In this problem, point O is located outside the circle with a radius of 6 cm and a distance of 10 cm from the center of the circle.
Key Points:
- A tangent is a line that touches a circle at exactly one point.
- The distance from the center of the circle to the point where the tangent touches the circle is equal to the radius of the circle.
Calculation:
To find the number of tangents that can be drawn from point O to the circle, we need to consider the different positions of point O.
1. When point O is inside the circle:
In this case, no tangents can be drawn from point O to the circle. This is because all lines drawn from a point inside a circle to the circle will intersect the circle at two points, not just one.
2. When point O is on the circle:
In this case, only one tangent can be drawn from point O to the circle. The tangent line will touch the circle at the point where point O is located.
3. When point O is outside the circle:
In this case, two tangents can be drawn from point O to the circle. The tangents are drawn in such a way that they touch the circle at two different points.
Therefore, the correct answer is option D - 2 tangents can be drawn from point O to the circle.
When a line is drawn from a point outside a circle to the circle, it is called a tangent. The tangent line touches the circle at exactly one point.
In this problem, point O is located outside the circle with a radius of 6 cm and a distance of 10 cm from the center of the circle.
Key Points:
- A tangent is a line that touches a circle at exactly one point.
- The distance from the center of the circle to the point where the tangent touches the circle is equal to the radius of the circle.
Calculation:
To find the number of tangents that can be drawn from point O to the circle, we need to consider the different positions of point O.
1. When point O is inside the circle:
In this case, no tangents can be drawn from point O to the circle. This is because all lines drawn from a point inside a circle to the circle will intersect the circle at two points, not just one.
2. When point O is on the circle:
In this case, only one tangent can be drawn from point O to the circle. The tangent line will touch the circle at the point where point O is located.
3. When point O is outside the circle:
In this case, two tangents can be drawn from point O to the circle. The tangents are drawn in such a way that they touch the circle at two different points.
Therefore, the correct answer is option D - 2 tangents can be drawn from point O to the circle.
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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)1b)3c)Infinited)2Correct answer is option 'D'. Can you explain this answer?
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