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Two circles of radius 37 cm and 20 cm intersect each other at P and Q. O and O’ are the centres of the circles. If the length of PQ is 24 cm, then the distance between their centre is:
- a)35 cm
- b)51 cm
- c)21 cm
- d)16 cm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two circles of radius 37 cm and 20 cm intersect each other at P and Q...
OP = 37 cm and O P = 20 cm
PQ = 24 cm
PM = MQ = 12 cm
OM = 35 cm
O'M = 16 cm
OO' = OM 4 + O’M
OO’ = 35 + 16 = 51 cm
Most Upvoted Answer
Two circles of radius 37 cm and 20 cm intersect each other at P and Q...
Given:
Radius of circle O = 37 cm
Radius of circle O' = 20 cm
Length of PQ = 24 cm
To find:
Distance between the centers of the two circles (OO')
Approach:
We can use the Pythagorean theorem to solve this problem. Let's consider the right-angled triangle formed by the centers of the two circles (OO') and the point of intersection (PQ). Using this triangle, we can calculate the distance between the centers.
Solution:
1. Let's start by drawing a diagram to visualize the problem.
- Draw two circles with radii 37 cm and 20 cm, respectively.
- Mark the centers of the circles as O and O'.
- Draw a line segment PQ of length 24 cm passing through the point of intersection of the circles (P and Q).
2. Identify the triangle formed by the centers of the circles and the point of intersection.
- Triangle OPO' is formed by the centers O and O' and the point of intersection P.
3. Apply the Pythagorean theorem to find the distance between the centers.
- In triangle OPO':
- OP^2 = OO'^2 + O'P^2 (By Pythagorean theorem)
- OP^2 = (37 cm)^2 + (20 cm)^2
- OP^2 = 1369 cm^2 + 400 cm^2
- OP^2 = 1769 cm^2
- Since OP = PQ = 24 cm (given),
- 24^2 = 1769 cm^2
- 576 = 1769 cm^2
- 1769 - 576 = 1193 cm^2
- OP^2 - PQ^2 = OO'^2
- 1193 cm^2 = OO'^2
- Take the square root of both sides to find the distance between the centers.
- √1193 cm = OO'
- OO' ≈ 34.5 cm
4. Round off the answer to the nearest whole number.
- The distance between the centers of the two circles is approximately 35 cm.
Therefore, the correct answer is option 'B' (35 cm).
Radius of circle O = 37 cm
Radius of circle O' = 20 cm
Length of PQ = 24 cm
To find:
Distance between the centers of the two circles (OO')
Approach:
We can use the Pythagorean theorem to solve this problem. Let's consider the right-angled triangle formed by the centers of the two circles (OO') and the point of intersection (PQ). Using this triangle, we can calculate the distance between the centers.
Solution:
1. Let's start by drawing a diagram to visualize the problem.
- Draw two circles with radii 37 cm and 20 cm, respectively.
- Mark the centers of the circles as O and O'.
- Draw a line segment PQ of length 24 cm passing through the point of intersection of the circles (P and Q).
2. Identify the triangle formed by the centers of the circles and the point of intersection.
- Triangle OPO' is formed by the centers O and O' and the point of intersection P.
3. Apply the Pythagorean theorem to find the distance between the centers.
- In triangle OPO':
- OP^2 = OO'^2 + O'P^2 (By Pythagorean theorem)
- OP^2 = (37 cm)^2 + (20 cm)^2
- OP^2 = 1369 cm^2 + 400 cm^2
- OP^2 = 1769 cm^2
- Since OP = PQ = 24 cm (given),
- 24^2 = 1769 cm^2
- 576 = 1769 cm^2
- 1769 - 576 = 1193 cm^2
- OP^2 - PQ^2 = OO'^2
- 1193 cm^2 = OO'^2
- Take the square root of both sides to find the distance between the centers.
- √1193 cm = OO'
- OO' ≈ 34.5 cm
4. Round off the answer to the nearest whole number.
- The distance between the centers of the two circles is approximately 35 cm.
Therefore, the correct answer is option 'B' (35 cm).
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Two circles of radius 37 cm and 20 cm intersect each other at P and Q. O and O’ are the centres of the circles. If the length of PQ is 24 cm, then the distance between their centre is:a)35 cmb)51 cmc)21 cmd)16 cmCorrect answer is option 'B'. Can you explain this answer?
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