Cycles of the hyperbolic plane of positive curvature

Properties of hyperbolic and elliptic cycles of the hyperbolic plane $\widehat H$ of positive curvature are investigated. An analog of Pythagorean theorem for a right trivertex with a parabolic hypotenuse is proved. For each type of straight lines, formulas expressing the length of a chord of a hyperbolic cycle in terms of the cycle radius, the measure of the central angle corresponding to the chord, and the radius of curvature of $\widehat H$ are obtained. The plane $\widehat H$ is considered in projective interpretation.