On circle, Draw line segments from, O, to, Y, from, K, to, Y, from, E, to, Y, & from, P, to, Y. Proof: circle has: O, Y, = K, Y, =, E, Y, =, P, Y, and labeled, (All Radii are =. Definition of a circle
Proof: Second circle added in row, has, arc, P, Q, =, arc, E, K, labeled, (Given).
Proof: Third circle added in row, has, angle, P, Y, O, = arc, P, O, labeled, (Intercepted arc). Fourth circle, added in row, has angle, E, Y, K, = arc, E, K, labeled, (Equal Central Angle).
Proof: fifth circle below left three circles, has angle, P, Y, O, = angle, E, Y, K, labeled, (Transitive Property). An arrow from circle 2, 3, and 4 point to Circle 5.
Proof: sixth circle below the first and second circles, has triangle, P, Y, O, = triangle, E, Y, K, labeled, (S, A, S). An arrow from Circle 1 and circle 5 point to Circle 6.
Proof: seventh circle below sixth circle, has segment, P, O, = segment, E, K, labeled, (congruent triangle yields congruent parts).