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

Question

Fed [463]

2 years ago

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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 commo

n chord

Mathematics

1 answer:

antoniya [11.8K] · Answer 1 · 2023-03-16T00:23:39+03:00

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.

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