AMO 2025 – Secondary 4 (Grade 10) Question 5

Question 5

An equilateral triangle has side a and an incircle. In each corner region, a smaller circle is tangent to the two adjacent sides and to the incircle. Find the combined area of the three smaller circles.

Question illustration

$3\pi a^2/14$
$\pi a^2/\sqrt3$
$\pi a^2/36$
$3\pi a^2\sqrt3/18$