On a football field, a ball is placed next to a corner flag. The pole of the corner flag is $1.25 \mathrm{~m}$ high, and the shadow of the pole is $1 \mathrm{~m}$. The farthest point of the ball's shadow is $23 \mathrm{~cm}$ away from the point where the ball touches the ground. What is the diameter of the ball?
If $A$ denotes the farthest point of the ball's shadow, $C$ the point of contact between the ball and the ground, $O$ the center of the ball, and $B$ the point on the vertical $O C$ axis of the ball whose shadow falls on $A$, then the triangle $A B C$ is similar to the right-angled triangle defined by the flagpole and its shadow. From this, and through some further similarities, we obtain - using the Pythagorean theorem multiple times, or with the help of trigonometric functions - that the diameter of the ball is approximately $22 \mathrm{~cm}$.