SOLUTION: Topic: Similarities (I don't know if proofs is the right section)
Chord AB on circle C of radius 3 intersects at diameter X. If AX = 3...
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Chord AB on circle C of radius 3 intersects at diameter X. If AX = 3...
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Question 1177020: Topic: Similarities (I don't know if proofs is the right section)
Chord AB on circle C of radius 3 intersects at diameter X. If AX = 3...
https://media.discordapp.net/attachments/802751414874537995/821169136516071424/R7QsDYgAAAABJRU5ErkJggg.png Answer by greenestamps(13203) (Show Source):
Label the endpoints of the diameter D and E, with D the endpoint closer to B.
Let x be the length of CX that we are to find.
Then CD is 3-x and CE is 3+x.
When two chords intersect inside a circle, the product of the lengths of the two parts of one chord is equal to the product of the lengths of the two parts of the other chord.
In this problem, that gives us
That equation is easily solved to find the answer to the problem.
