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. Wetzel[5] proved if is a closed curve of length L inE n , then lies in some ball of radius [ L=4]. In this paper, we gener-alize Wetzel’s result to the non-Euclidean plane with much strongerversion. That is to develop a lower bound of length of a triangleinscribed in a circle in non-Euclidean plane in terms of a chord ofthe circle. 1. IntroductionThe problem concerning the smallest circle containing copies of allclosed curves of given length, has been studied from time to time. Amongthem Wetzel[5] proved the following results:If is an arc [closed curve] of length Lin E n , then lies in someball of radius L=2[L=4]. If no smaller ball covers , then is a segmentof length L[L=2 traversed twice].The circumscribed circle of a plane curve has to meet the curve in aset of points of which convex hull contains the center of the circumcir-cle. So there must be a triangle with vertices on the intersection of thecurve with the circle and having the center of the circle in its interior.

LOWER BOUND OF LENGTH OF TRIANGLE INSCRIBED IN A CIRCLE ON NON-EUCLIDEAN SPACES