Two chords of length 9 and 17 are drawn from one point of the circle.

| June 22, 2021 | education

Two chords of length 9 and 17 are drawn from one point of the circle. Find the length of this circle if the distance between the midpoints of the chords is 5.

Let the points D and E be the middle of the chords AC and BC, then the segment DE is the middle line of the triangle ABC, then AB = 2 * DE = 2 * 5 = 10 cm.

Knowing the lengths of the sides of the triangle ABC, we determine its area by Heron’s theorem.

The half-perimeter of the triangle is: p = (17 + 9 + 10) / 2 = 18 cm.

Then Sav = √18 * (18 – 17) * (18 – 10) * (18 – 9) = √18 * 1 * 8 * 9 = √1296 = 36 cm2.

Determine the radius of the circumscribed circle around the triangle ABC.

R = AB * BC * AC / 4 * Savs = 10 * 9 * 17/4 * 36 = 1530/144 = 10.625 cm.

Then D = 2 * R = 2 * 10.625 = 21.25 cm.

Answer: The diameter of the circle is 21.25 cm.



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