In a circle of radius r there are two parallel chords.
The distance between the chords is equal to the average of the lengths of the chords.
Find the relation between the distances from the chords to the center of the circle.
Say the chords are horizontal. Let the length of the uppermost be 2x and the other 2y so that the distance between them is x+y.
A vertical line through the origin cuts the chords in half. The distance from the origin to the point where the chords intersect the circle is r. If the distance of the top chord to the origin is d then the distance of the other chord from the radius (x+y-d).
Then we have two right triangles and two expressions for r^2.
r^2 = x^2 + d^2 = y^2 + (x + y - d)^2
which easily simplifies to d=y.
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Posted by xdog
on 2022-02-11 11:10:31 |
algebraic solution
