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The New Proof of Ptolemy’s Theorem & Nine Point Circle Theorem
Mathematics and Computer Science
Volume 1, Issue 4, November 2016, Pages: 93-100
Received: Aug. 31, 2016; Accepted: Oct. 18, 2016; Published: Dec. 14, 2016
Author
Dasari Naga Vijay Krishna, Department of Mathematics, Narayana Educational Instutions, Bengalore, India
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Abstract
The main purpose of the paper is to present a new proof of the two celebrated theorems: one is “Ptolemy's Theorem” which explains the relation between the sides and diagonals of a cyclic quadrilateral and another is “Nine Point Circle Theorem” which states that in any arbitrary triangle the three midpoints of the sides, the three feet of altitudes, the three midpoints of line segments formed by joining the vertices and Orthocenter, total nine points are concyclic. Our new proof is based on a metric relation of circumcenter.
Keywords
Ptolemy’s Theorem, Circumcenter, Cyclic Quadrilateral, Nine Point Circle Theorem, Pedals Triangle, Medial Triangle
Dasari Naga Vijay Krishna, The New Proof of Ptolemy’s Theorem & Nine Point Circle Theorem, Mathematics and Computer Science. Vol. 1, No. 4, 2016, pp. 93-100. doi: 10.11648/j.mcs.20160104.14
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