Check the picture below.
so let's take a peek at the top section of the picture.
drawing a circle stemming from C that'd be tangent to AB will look like that, and the circle will hit AC and BC at those points making the green line you see there.
One thing to be noteworthy about that line is that, it has on the upper side an inscribed right-angle, if that's so by "Thales Theorem", that's a flag that the green line is really a line of the semi-circle and thus is really the diametrical line of the circle, well, if we draw a line from C down to AB perpendicularly pretty much, we'd end up with the red line you see there, which is also a diametrical line to the circle.
what the hell all that means? Well, it means that the red line and green line are both diametrical and thus equal, now let's get the length of the red line.
now let's take a peek at the bottom section of the picture.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.
