let formula_13 be a triangle in a circle where formula_14 is a diameter in that circle. then construct a new triangle formula_15 by mirroring triangle formula_13 over the line formula_14 and then mirroring it again over the line perpendicular to formula_14 which goes through the center of the circle. since lines formula_19 and formula_20 are parallel, likewise for formula_21 and formula_22, the quadrilateral formula_23 is a parallelogram. since lines formula_14 and formula_25 are both diameters of the circle and therefore are equal length, the parallelogram must be a rectangle. all angles in a rectangle are right angles.