CIRCUMFERENCE DRAWING

The most common way to draw a circle is using a compass, but it's not very fun to do that, so here's another way to draw circles, or at least pieces of them.

These mechanisms rely on the Capable Arc Theorem. To see it applied, we fix a circle and also a chord of the same circle. As the chord divides the circle into two arcs, we can choose one of them and take any point on it. Hence, the theorem says that the angle that these points make with the two ends of the string is always the same.

The mechanism then does the opposite: it fixes the angle with two rays, forces them to pass through the ends of the chord and the vertex traces the arc of the circle! The video below shows a little bit of how this mechanism works.

USEFUL LINKS

As said, it is possible to draw a capable arc without using this piece, just using a ruler and compass. This UFSCar (São Carlos Federal University) article explains step by step how to do this and, at the end, shows how it was supposed to be. Try to build the requested arch and, who knows, even others with different angulations!

Capable bow is the denomination of a certain bow. The chord of the circle where the arc ends is seen from any point on the arc at the same angle, which is called an inscribed angle. This Wikipedia page talks about that angle, explaining, from a slightly different point of view, the capable bow we're used to.

If we are talking about the locus of the points that see a certain segment, we are talking about a pair of capable arcs, instead of just one. This D!namática page explains what these arches are, in addition to bringing an interactive screen that allows you to change the angles and position of the point involved in the construction!

And since we talked about drawing circles, this InfoEscola page brings some information about the circumference and its elements, in addition to explaining some concepts and formulas involved in its study. The page also has some exercises on the topic that can be performed to improve knowledge!