Answer:
[tex]BD=11\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
we know that
[tex]AE(EC)=BE(ED)[/tex] ----> by Intersecting Chords Theorem
substitute the given values
[tex]x(x+12)=(x+2)(x+5)[/tex]
[tex]x^2+12x=x^2+5x+2x+10[/tex]
[tex]12x=7x+10\\12x-7x=10\\5x=10\\x=2\ units[/tex]
Find the value of BD
[tex]BD=BE+ED[/tex] ----> by addition segment postulate
[tex]BD=(x+2)+(x+5)[/tex]
[tex]BD=2x+7[/tex]
substitute the value of x
[tex]BD=2(2)+7=11\ units[/tex]
