## 107. Math Puzzle $4 / 74$

What is the distance of a $6 \mathrm{~cm}$ long chord from the center of a circle with a radius of $5 \mathrm{~cm}$?
The center of the circle $M$ is connected to the endpoints $A$ and $B$ of the chord, and a perpendicular is dropped from $M$ to the chord. Let the desired distance be $x = MD$.

In the right-angled triangle $ADM$, by Pythagoras: $AM^2 = AD^2 + DM^2$ or $5^2 = 3^2 + x^2$, i.e., $x = 4 \text{ cm}$. The chord is thus $4 \text{ cm}$ away from the center of the circle.