Three circles, three tangent lines, and a suspicious straight line
Draw three circles of different sizes, none inside another. For each pair of circles, draw the two lines that touch both circles from the outside without crossing between them, and mark where each pair of those tangent lines crosses. Do the three crossing points, one per pair of circles, have to line up?
Reveal the answer
Yes, always, exactly on one straight line, no matter the circles' sizes or positions. This is Monge's theorem, named for the French mathematician Gaspard Monge, who proved it in the early 1800s using a clever trick: imagining the three flat circles as the equators of three spheres of different sizes stacked in 3D space, where the collinearity becomes almost obvious before being translated back down to the flat page.