Padyala, Radhakrishnamurty
(2021)
An easy proof of Ptolemy’s theorem.
At Right Angles.
pp. 66-68.
ISSN 2582-1873
Abstract
Many proofs are available for
the famous and important theorem in geometry
known as Ptolemy’s theorem. For our discussion,
we consider the proof presented by Shirali. In his
article, he described a simple geometrical proof of the
theorem and presented two elegant applications. He noted
that the proof ‘presents a challenge’ because from the
statement of the theorem we get no clue on how to tackle it.
In the proof, there arises a crucial idea of locating a point E
on a diagonal of the quadrilateral that enables the
construction of two similar triangles. A recent demonstration
by Tunsteno demonstrates a simple and intuitively
appealing method for locating the point E. We present it
here for the benefit of school students and teachers.
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