VTMO 2026 - Grade 9 - Semifinal - SET 3 - Self-study Question 16

Question 16

Square ABCD has side AB=2. Three circles, with centres $O_1,O_2,O_3$ and the same radius r, lie inside it. Circle $O_1$ touches AB,AD and circle $O_3$; circle $O_2$ touches AB,BC and circle $O_3$; circle $O_3$ touches CD and the other two circles. Find r.

Question illustration

$\sqrt5-2$
$5-2\sqrt5$
$\frac{\sqrt3}{4}$
$\frac{3\sqrt2}{8}$
$\frac12$