IKMC 2015 - Grades 11-12 - Self-study Question 9

Question 9

The diameters of three semicircles are the sides of a right triangle. Their areas are X, Y and Z square centimetres as shown. Which relation is necessarily true?

Question illustration

$X+Y<Z$
$\sqrt X+\sqrt Y=\sqrt Z$
$X+Y=Z$
$X^2+Y^2=Z^2$
$X^2+Y^2=Z$