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... https://media.discordapp.net/attachmen

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): You can put this solution on YOUR website!

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.

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