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A chord of length 30 cm is at a distance of 8 cm from the centre of a circle. The radius of the circle is: (SSC CGL 1st Sit. 2013)
- a)19
- b)17
- c)23
- d)21
Correct answer is option 'B'. Can you explain this answer?
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A chord of length 30 cm is at a distance of 8 cm from the centre of a ...
To find the radius of the circle, we can use the Pythagorean theorem. Let's break down the problem into smaller steps:
1. Identify the given information:
- Length of the chord = 30 cm
- Distance of the chord from the center = 8 cm
2. Understand the problem:
We need to find the radius of the circle. Since the chord is at a distance of 8 cm from the center, it divides the diameter into two equal parts. We can draw a right angle triangle using the radius, the distance from the center to the chord, and half of the chord length.
3. Use the Pythagorean theorem:
According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's assume the radius of the circle as 'r'. Then, the distance from the center to the chord (which is perpendicular to the chord) is also 'r'. And half of the chord length is 15 cm.
Applying the Pythagorean theorem:
r^2 = (8 cm)^2 + (15 cm)^2
r^2 = 64 cm^2 + 225 cm^2
r^2 = 289 cm^2
Taking the square root on both sides, we get:
r = √289 cm
r = 17 cm
4. Answer:
The radius of the circle is 17 cm. Therefore, the correct answer is option 'B'.
1. Identify the given information:
- Length of the chord = 30 cm
- Distance of the chord from the center = 8 cm
2. Understand the problem:
We need to find the radius of the circle. Since the chord is at a distance of 8 cm from the center, it divides the diameter into two equal parts. We can draw a right angle triangle using the radius, the distance from the center to the chord, and half of the chord length.
3. Use the Pythagorean theorem:
According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's assume the radius of the circle as 'r'. Then, the distance from the center to the chord (which is perpendicular to the chord) is also 'r'. And half of the chord length is 15 cm.
Applying the Pythagorean theorem:
r^2 = (8 cm)^2 + (15 cm)^2
r^2 = 64 cm^2 + 225 cm^2
r^2 = 289 cm^2
Taking the square root on both sides, we get:
r = √289 cm
r = 17 cm
4. Answer:
The radius of the circle is 17 cm. Therefore, the correct answer is option 'B'.
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Community Answer
A chord of length 30 cm is at a distance of 8 cm from the centre of a ...
Here chord AB = 300 cm
AD = 15 cm
OD = 8 cm
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A chord of length 30 cm is at a distance of 8 cm from the centre of a circle. The radius of the circle is: (SSC CGL 1st Sit. 2013)a)19b)17c)23d)21Correct answer is option 'B'. Can you explain this answer?
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