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Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is.
- a)√7 cm
- b)3√7 cm
- c)4√7 cm
- d)(8 + 2√7) cm
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Two circles of radii 10 cm and 8 cm intersect each other and the lengt...
M is the mid-point of AB,
∴ AM = 6 cm
AO (r1) = 10 cm,
AO' (r2) = 8 cm
AB is perpendicular to OO' , then
In ΔAOM, 100 = 36 + OM2 [using pythagoras theorem]
⇒ OM = 8 cm; In ΔAMO', 64 = 36 + MO'2
⇒ √28 = MO' = 2√7 = MO'
∴ OO' = (2√7 + 8) cm
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Two circles of radii 10 cm and 8 cm intersect each other and the lengt...
To find the distance between the centers of the two circles, we can draw a line connecting the centers and draw a perpendicular line from the center of one circle to the common chord.
Let O1 be the center of the larger circle with radius 10 cm, and O2 be the center of the smaller circle with radius 8 cm. Let AB be the common chord, with length 12 cm.
Since the common chord is perpendicular to the line connecting the centers, we can draw a right triangle O1O2B, where O1O2 is the distance between the centers and O1B and O2B are the radii of the circles.
Using the Pythagorean theorem, we can find the length of O1O2:
O1O2^2 = O1B^2 + O2B^2
O1O2^2 = 10^2 + 8^2
O1O2^2 = 164
Taking the square root of both sides, we find:
O1O2 = √164
O1O2 = 2√41
Therefore, the distance between the centers of the two circles is 2√41 cm.
Let O1 be the center of the larger circle with radius 10 cm, and O2 be the center of the smaller circle with radius 8 cm. Let AB be the common chord, with length 12 cm.
Since the common chord is perpendicular to the line connecting the centers, we can draw a right triangle O1O2B, where O1O2 is the distance between the centers and O1B and O2B are the radii of the circles.
Using the Pythagorean theorem, we can find the length of O1O2:
O1O2^2 = O1B^2 + O2B^2
O1O2^2 = 10^2 + 8^2
O1O2^2 = 164
Taking the square root of both sides, we find:
O1O2 = √164
O1O2 = 2√41
Therefore, the distance between the centers of the two circles is 2√41 cm.
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Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is.a)√7 cmb)3√7 cmc)4√7 cmd)(8 + 2√7) cmCorrect answer is option 'D'. Can you explain this answer?
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Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is.a)√7 cmb)3√7 cmc)4√7 cmd)(8 + 2√7) cmCorrect answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is.a)√7 cmb)3√7 cmc)4√7 cmd)(8 + 2√7) cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two circles of radii 10 cm and 8 cm intersect each other and the length of common chord is 12 cm. The distance between their centres is.a)√7 cmb)3√7 cmc)4√7 cmd)(8 + 2√7) cmCorrect answer is option 'D'. Can you explain this answer?.
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