AMO 2024 – Secondary 4 (Grade 10) Question 4

Question 4

Two windshield wipers each have length $L$ and sweep the upper semicircles shown. Their pivot separation is $O_1O_2=L$. What is the total area swept by at least one wiper?

Question illustration

$\frac{\sqrt3}2\pi L^2$
$(\frac{2\pi}3+\frac{\sqrt3}4)L^2$
$\pi L^2-\frac{L^2\sqrt3}4$
$\frac{2\pi L^2}3$