A circle with center O has integer diameter. A point P is selected inside the circle such that OP = 12 and there are 5 chords of integer length passing through P with respect to the given circle. Then find the possible radii of all such circles.
(In reply to
re: Solution by Jer)
For the case D=74 and r=37:
Point P is at (12,0).
The y value which is on the circle with radius 37 is at (12, 35).
35 = √(37^2 - 12^2)
A chord through P and perpendicular to the x-axis has length 70.
Another chord through P but identical to the x-axis has length 74.
So we have chords of 70 and 74. Continuously varying the angle between the chord and the x-axis should account for every chord length between 70 and 74 which includes the integers 71,72,73.
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Posted by Larry
on 2024-12-06 12:04:56 |
re(2): Solution
