Question 1177020
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Label the endpoints of the diameter D and E, with D the endpoint closer to B.<br>
Let x be the length of CX that we are to find.<br>
Then CD is 3-x and CE is 3+x.<br>
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.<br>
In this problem, that gives us<br>
{{{(3-x)(3+x) = 2*3}}}<br>
That equation is easily solved to find the answer to the problem.<br>