Question

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?

Answer 1

11

Explanation:

Answer 2

`BD=11\ units`

Explanation:

The picture of the question in the attached figure

we know that

`AE(EC)=BE(ED)`----> by Intersecting Chords Theorem

substitute the given values

`x(x+12)=(x+2)(x+5)\\x^2+12x=x^2+5x+2x+10\\12x=7x+10\\12x-7x=10\\5x=10\\x=2\ units`

Find the value of BD

`BD=BE+ED` ----> by addition segment postulate

`BD=(x+2)+(x+5)\\BD=2x+7`

substitute the value of x

`BD=2(2)+7=11\ units`