SOLUTION: Two parallel chords of length 24cm and 10cm which lie on opposite sides of a circle are 17cm apart. Calulate the radius of the circle to the nearest wholenumber.

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Question 1182839: Two parallel chords of length 24cm and 10cm which lie on opposite sides of a circle are 17cm apart. Calulate the radius of the circle to the nearest wholenumber.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let, radius of the circle ber cm.
Suppose, the 10 cm long chord is x cm away from the center.
Thus, the 24 cm long chord should be %2817+-+x%29 cm away from the center.

We know, perpendicular drawn from center on any chord bisects the latter.

Thus,
+r%5E2+=+x%5E2+%2B+%2810%2F2%29%5E2+=+x%5E2+%2B+5%5E2
+r%5E2+=+%2817+-+x%29%5E2+%2B+%2824%2F2%29%5E2+=+%2817+-+x%29%5E2+%2B+12%5E2

Thus,
+x%5E2+%2B+5%5E2+=+%2817+-+x%29%5E2+%2B+12%5E2
+x%5E2+-+%2817+-+x%29%5E2+=+12%5E2+-+5%5E2
17+%2A+%282x+-+17%29+=+17+%2A+7
+%282x+-+17%29+=+7
2x+=+24
x+=+12

So,
r%5E2+=+12%5E2+%2B+5%5E2+=+144+%2B+25+=+169
+r+=+13
The answer is: the radius of the circle is 13 cm