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Question 1178915: Segment AB is trisected at its
points of intersection with
concentric circles of radius 7cm
and 9cm. Find the length of
segment AB.
https://media.discordapp.net/attachments/769181283913695264/833885965344440350/unknown.png
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Call the center of the circles O.
Let points C and D be the points of intersection of AB with the smaller circle.
Let point E be on AB such that OE is perpendicular to AB.
By symmetry, CE=DE; let that length be x (i.e., CD=2x).
C and D trisect AB, so AC=DB=2x.
Use the Pythagorean Theorem on triangles OED and OEB to get two equations in x^2 and y^2. Those two equations are easily solved for x, leading immediately to the answer to the problem.
I leave it to you to do the work to finish.
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