This proposition constructs a line segment perpendicular to given line segment from a not on it. The way this is done is similar to the previous proposition, except the triangle constructed isn't necessarily equilateral. This makes sense because in the last few propositions, equilateral triangles were constructed because they have all three sides congruent, but in reality, onto two of those congruent sides were leveraged. To be able to leverage some symmetry, it is required that the triangle constructed is at least isosceles. This property can be encoded by drawing a circle around C, and stating that the other two vertices must lie on that circle. The radius of this circle must be large enough so that the circle intersects with AB. To construct this requirement geometrically, Euclid selects a point D on the opposite side of EF as C, so that CD is the radius. Taking the intersection between this circle and AB yields E and F, and EF is bisected at H. While it might not look like it because the way the Poincare Disk warps space, this construction creates a line of symmetry, CH. Its then easy to prove that CH is perpendicular to AB.