The points AB are also located on another circle, centered on the Moon. The radius in that case is the distance $$R$$ to the Moon, and because the arc AB covers 0.1 degrees, we get $AB\,=\,\frac{2\pi r}{360}\times 0.1$
Strictly speaking, each of the two arcs AB expressed in the above equations is measured along a different circle, with a different radius (and the two circles curve in opposite ways). However, in both cases AB covers only a small part of the circle, so that as an approximation we may regard each of the arcs as equal to the straight-line distance AB. That assumption allows us to regard the two expressions as equal and to write $\frac{2\pi r}{360}\times 0.1\,=\,\frac{2\pi r}{360}\times 9$
Multiplying both sides by 360 and dividing by $$2\pi$$ give $0.1R\,=\,9r\,\Rightarrow\,\frac{R}{r}\,=\,90$ suggesting the Moon's distance is 90 Earth radii, an overestimate of about 50%.