Abstract
We consider some applications of Ptolemy's theorem. In particular, we nd a criterion for constructing an inscribed hexagon.
Highlights
Today, to improve the quality of teaching mathematics is one of biggest challenges faced in the field of education
The criterion for an inscribed rectangle provided in modern textbooks of secondary school geometry involves internal angles of rectangle
We consider some problems which have been earlier solved by traditional methods, and we solve these problems by using new approaches, namely, Ptolemy’s theorem
Summary
To improve the quality of teaching mathematics is one of biggest challenges faced in the field of education. It says: for a rectangle to be inscribed in a circle, it is necessary and sufficient that the sum of its opposite angles be equal to 180◦. Not included in modern school textbooks, Ptolemy’s theorem is a good criterion for constructing an inscribed rectangle which involves the sides and diagonals of a rectangle.
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