Question

Let $AB$ and $CD$ be two chord of a circle such that $AB$ bisect the chord $CD$ at $E$. If $AE\cdot EB=36$, then $CD=$units

Answer 1

For a given circle if two chords are intersecting each other then the multiplication of their segments are equal.
Now $AB$ bisected the chord $CD$ at $E$
$\therefore CD=2DE=2EC$
Now as we know
$AE\cdot EB=DE\cdot EC=(DE{)}^2\Rightarrow DE=6\text{units}$
Hence $CD=12$ units