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From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is
- a)7 cm
- b)12 cm
- c)15 cm
- d)24.5 cm.
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
From a point Q, the length of the tangent to a circle is 24 cm and the...
Solution:
Given:
Length of the tangent = 24 cm
Distance of point Q from the center = 25 cm
To find:
Radius of the circle
Explanation:
In a circle, a tangent is a line that touches the circle at only one point. The point where the tangent touches the circle is called the point of tangency.
We are given the length of the tangent as 24 cm. Let's call the point where the tangent touches the circle as point P.
1. Draw a diagram:
Draw a circle with the center C. Draw the tangent line PQ from point Q to point P on the circle.
2. Identify the given information:
Given:
Length of tangent PQ = 24 cm
Distance of point Q from the center = 25 cm
3. Use the properties of tangents:
The length of the tangent from an external point to a circle is the same for both tangents drawn from that point.
4. Apply the tangent property:
The length of tangent PQ = Length of tangent PR
5. Find the distance of point R from the center:
Since the lengths of the tangents from an external point to a circle are equal, the distance of point R from the center will be the same as the distance of point Q from the center.
Distance of point R from the center = 25 cm
6. Find the radius of the circle:
The radius of the circle is the distance from the center to any point on the circle.
Using Pythagoras theorem, we can find the radius of the circle:
(Radius)^2 = (Distance of point R from the center)^2 - (Length of tangent)^2
(Radius)^2 = 25^2 - 24^2
(Radius)^2 = 625 - 576
(Radius)^2 = 49
Radius = √49
Radius = 7 cm
Therefore, the radius of the circle is 7 cm, which is option A.
Given:
Length of the tangent = 24 cm
Distance of point Q from the center = 25 cm
To find:
Radius of the circle
Explanation:
In a circle, a tangent is a line that touches the circle at only one point. The point where the tangent touches the circle is called the point of tangency.
We are given the length of the tangent as 24 cm. Let's call the point where the tangent touches the circle as point P.
1. Draw a diagram:
Draw a circle with the center C. Draw the tangent line PQ from point Q to point P on the circle.
2. Identify the given information:
Given:
Length of tangent PQ = 24 cm
Distance of point Q from the center = 25 cm
3. Use the properties of tangents:
The length of the tangent from an external point to a circle is the same for both tangents drawn from that point.
4. Apply the tangent property:
The length of tangent PQ = Length of tangent PR
5. Find the distance of point R from the center:
Since the lengths of the tangents from an external point to a circle are equal, the distance of point R from the center will be the same as the distance of point Q from the center.
Distance of point R from the center = 25 cm
6. Find the radius of the circle:
The radius of the circle is the distance from the center to any point on the circle.
Using Pythagoras theorem, we can find the radius of the circle:
(Radius)^2 = (Distance of point R from the center)^2 - (Length of tangent)^2
(Radius)^2 = 25^2 - 24^2
(Radius)^2 = 625 - 576
(Radius)^2 = 49
Radius = √49
Radius = 7 cm
Therefore, the radius of the circle is 7 cm, which is option A.
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From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle isa)7 cmb)12 cmc)15 cmd)24.5 cm.Correct answer is option 'A'. Can you explain this answer?
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