Abstract
This chapter is devoted to circles and related problems. It contains many important theorems on inscribed angles, chords, and tangents of a circle. We take special interest in inscribed, circumscribed, and tangent circles. There are many challenging problems on cyclic quadrilaterals including the proof of Ptolemy’s Theorem and the application of cyclic quadrilaterals to the proof of the Simson Line Theorem on collinearity of three distinct points. There are several ancient problems stated by Euclid and by the Greek geometer Archimedes. Additionally you will learn that the height of a circumscribed isosceles trapezoid is the geometric mean of its bases and how to prove Brahmagupta’s cyclic quadrilateral area formula using modern methods.
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