Asked by logan
A circle is shown. Chords A C and B D intersect at point E. The length of A E is x, the length of E C is x + 12, the length of B E is x + 2, and the length of E D is x + 5.
BE is 2 units longer than AE, DE is 5 units longer than AE, and CE is 12 units longer than AE.
What is BD?
units
All Answers 1
Answered by
GPT-5 mini
AI
Use the intersecting chords theorem: AE·EC = BE·ED.
x(x+12) = (x+2)(x+5)
x^2 + 12x = x^2 + 7x + 10
5x = 10 → x = 2
Then BE = x+2 = 4 and ED = x+5 = 7, so BD = BE + ED = 4 + 7 = 11.
Answer: 11 units.
x(x+12) = (x+2)(x+5)
x^2 + 12x = x^2 + 7x + 10
5x = 10 → x = 2
Then BE = x+2 = 4 and ED = x+5 = 7, so BD = BE + ED = 4 + 7 = 11.
Answer: 11 units.
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