The radiuses of two intersecting circles are 17 and 39. The distance between their centers is 44. Find the length of their common chord

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01-01-2022
Mathematics

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The radiuses of two intersecting circles are 17 and 39. The distance between their centers is 44. Find the length of their common chord

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prabhseeratsandhu prabhseeratsandhu · Answer 1 · 2022-01-01T17:05:00+01:00

Answer:

If x is the distance from centre fo the circle, with radius 25cm, to its intersection point with the common chord, x²+24²=25² =>x=7cm.

Distance from this intersecting point to the centre of the other circle=39–7=32cm

Ratio of the sides of the right triangle thus formed is 24:32=3:4. Since 3:4:5 is the basic pythagorean triplet, the radius of the other circle=5*24/3=40cm.

Aliter: radius of the other circle=√32²+24²= 40cm.

The radiuses of two intersecting circles are 17 and 39. The distance between their centers is 44. Find the length of their common chord

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