IKMC 2010 - Grades 11-12 - Paper 02 - Self-study Question 30

Question 30

Points P and Q are chosen on the two legs of a right triangle, whose leg lengths are a and b. Let K and H be the perpendicular feet from P and Q to the hypotenuse. What is the smallest possible value of $KP+PQ+QH$?

$a+b$
$\frac{2ab}{a+b}$
$\frac{2ab}{\sqrt{a^2+b^2}}$
$\frac{(a+b)^2}{\sqrt{a^2+b^2}}$
$\frac{(a+b)^2}{2ab}$