Asked by luhha
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 power-of-a-point relation for E: AE·BE = CE·DE. Let AE = x. Then
x(x+2) = (x+12)(x+5).
Solve: x^2+2x = x^2+17x+60 → -15x = 60 → x = -4.
Then BE = x+2 = -2 and DE = x+5 = 1, so BD = |BE - DE| = |(-2) - 1| = 3.
Answer: 3 units.
x(x+2) = (x+12)(x+5).
Solve: x^2+2x = x^2+17x+60 → -15x = 60 → x = -4.
Then BE = x+2 = -2 and DE = x+5 = 1, so BD = |BE - DE| = |(-2) - 1| = 3.
Answer: 3 units.
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