SOLUTION: A chord 30cm long is 20cm from the centre of a circle. Calculate the length of a chord which is 24cm from the centre

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Question 1087174: A chord 30cm long is 20cm from the centre of a circle. Calculate the length of a chord which is 24cm from the centre
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.
0.  First make a sketch.

    Find two right-angled triangles in the sketch.

    Then apply the Pythagorean theorem to these triangles.



1.  Find the radius of the circle from the first condition:

    R = sqrt%28%2830%2F2%29%5E2+%2B+20%5E2%29 = sqrt%2815%5E2+%2B+20%5E2%29 = sqrt%28225+%2B+400%29 = sqrt%28625%29 = 25 cm.



2.  Then calculate the length L of the another chord:

    L%2F2 = sqrt%28R%5E2+-+24%5E2%29 = sqrt%2825%5E2-24%5E2%29 = sqrt%28%2825-24%29%2A%2825%2B24%29%29 = sqrt%2849%29 = 7 cm.

Answer. L = 2*7 = 14 cm.

Solved.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Put center of the circle at the origin and make the chord 30 cm parallel to the x axis, and above the x-axis. Endpoints of this chord are (-15, 20) and (15, 20).

Radius:
r%5E2=15%5E2%2B20%5E2
r%5E2=225%2B400
r%5E2=625
-
x%5E2%2By%5E2=625


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Calculate the length of a chord which is 24cm from the centre.
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Endpoints of this chord, can be (x, 24) and (-x, 24).
x%5E2=625-y%5E2
x=sqrt%28625-24%5E2%29
x=sqrt%2849%29=7
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Length of chord, 2%2A7=highlight%2814%29
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