Find the diameter?

Relevant wiki: Circles - Intersecting Chords

Using intersecting chord theorem, we know that the product of the two segments of the chord (20x20) is equal to the product of the two segments of the diameter (10x ?).

20x20 = 10x?

400 = 10x?

400 = 10x40

D = 10+40 = 50

Consider the diagram on the left.

$r^2=(r-10)^2+20^2$

$r^2=r^2-20r+100+400$

$20r=500$

$r=25$

$diameter=2r=2(25)=$ $\boxed{50}$

$r^2-20^2=(r-10)^2$

$r^2-400=r^2-20r+100$

$20r=100+400$

$20r=500$

$r=25$

Diameter = $25\times2=\boxed{50}$