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Two parallel lines touch the circle at points A and B respectively, If area of the circle is 25πcm2, then AB is equal to
- a)5 cm
- b)8 cm
- c)10 cm
- d)25 cm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two parallel lines touch the circle at points A and B respectively, If...
Let radius of circle = R
∴ πR2 = 25π
⇒ R = 5cm
∴ Distance between two parallel tangents
= diameter = 2 x 5 = 10 cm.
∴ πR2 = 25π
⇒ R = 5cm
∴ Distance between two parallel tangents
= diameter = 2 x 5 = 10 cm.
Most Upvoted Answer
Two parallel lines touch the circle at points A and B respectively, If...
Since , Area = π ( r)2.
Therefore, radius of the circle = 5 cm .
Since two parallel lines touch the circle at A and B . Then Ab becomes the diameter.
So , AB = 10 cm
Therefore, radius of the circle = 5 cm .
Since two parallel lines touch the circle at A and B . Then Ab becomes the diameter.
So , AB = 10 cm
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Community Answer
Two parallel lines touch the circle at points A and B respectively, If...
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
Since the circle touches the two parallel lines at points A and B, the distance between these two points is equal to the diameter of the circle.
Let's say the distance between A and B is d, then the diameter of the circle is also d.
The radius of the circle is half the diameter, so the radius is d/2.
Using the formula for the area of a circle, we have:
A = π(d/2)^2
25 = π(d/2)^2
To solve for d, we can divide both sides of the equation by π:
25/π = (d/2)^2
Taking the square root of both sides:
√(25/π) = d/2
Multiplying both sides by 2:
2√(25/π) = d
Therefore, the distance between points A and B is 2√(25/π).
Since the circle touches the two parallel lines at points A and B, the distance between these two points is equal to the diameter of the circle.
Let's say the distance between A and B is d, then the diameter of the circle is also d.
The radius of the circle is half the diameter, so the radius is d/2.
Using the formula for the area of a circle, we have:
A = π(d/2)^2
25 = π(d/2)^2
To solve for d, we can divide both sides of the equation by π:
25/π = (d/2)^2
Taking the square root of both sides:
√(25/π) = d/2
Multiplying both sides by 2:
2√(25/π) = d
Therefore, the distance between points A and B is 2√(25/π).
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Two parallel lines touch the circle at points A and B respectively, If area of the circle is 25πcm2, then AB is equal toa)5 cmb)8 cmc)10 cmd)25 cmCorrect answer is option 'C'. Can you explain this answer?
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