Level 20: Construct a line (segment) tangent to both circles. Construct the outer tangent line.

Hint: Think ratios.

Solution: First construct the ray AB, and let the outer tangent line intersect AB at O. Now OA:OB should be (radius of A: radius of B). To find such point O, we use the similar triangle NAO and MBO. Once we found the point O, we need to find a point C on circle A such that OCA is a right angle. Now we leverage another fact, angle subtended by the diameter on a circle is the right angle, so we construct the midpoint P of O and A, draw the circle with center P and radius PA, so the intersection between the circle would give us the point C and we are done.