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In a diagram of circle, chords AB and CD

intersect at E. If AE = 3, EB = 4, CE = x, and ED = x - 4, what is the
value of x?

1 answer

you have similar triangles, so set up a ratio

(x-4)/4 = 3/x
x^2 - 4x = 12
x^2 - 4x - 12 = 0
(x-6)(x+2)= 0

x = 6 or x = -2, but x = -2 makes no sense

so x = 6

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