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.