Question 23032: Two chords, AB and CD, intersect in a circle at E. if _AE= 6cm, BE = 8 cm, and CE = 3(DE), what is the length of CD?
Answer by NaiXLG(18)   (Show Source):
You can put this solution on YOUR website! Its been a while since I've done this, so bear with me if the answer is kind of flawed.
From what I interpreted of the question, I got that:
(AB U CD) at E (U means intersects)
AE = 6cm
BE = 8cm
CE = 3DE
Replace your unknowns with x.
DE = x
and CE = 3DE = 3x
Now, use the property that says....(I think, check behind me)
(AE)(EB) = (CE)(ED)
So we have,
6 * 8 = 3x * x
48 = 3x^2
x^2 = 16
x = +/- 4
(discard the negative answer, because distance cannot be negative.)
Now, substitute back;
ED = x = 4
CE = 3x = 3(4) = 12
So CD = CE + ED
CD = 16
There you go!
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