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Circles
Circles

... o Tangents cross circle at 1 point whereas secants cross at 2. o Inscribed polygons are polygons within a circle with all vertices on the circle whereas circumscribed polygons are polygons that surround a circle with the circle touching all sides of the polygon. ICA Hints o pg 443  #1 Proof can be ...
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... G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Apply geometric concepts in modeling situations G-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or ...
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Rational trigonometry

Rational trigonometry is a proposed reformulation of metrical planar and solid geometries (which includes trigonometry) by Canadian mathematician Norman J. Wildberger, currently an associate professor of mathematics at the University of New South Wales. His ideas are set out in his 2005 book Divine Proportions: Rational Trigonometry to Universal Geometry. According to New Scientist, part of his motivation for an alternative to traditional trigonometry was to avoid some problems that occur when infinite series are used in mathematics. Rational trigonometry avoids direct use of transcendental functions like sine and cosine by substituting their squared equivalents. Wildberger draws inspiration from mathematicians predating Georg Cantor's infinite set-theory, like Gauss and Euclid, who he claims were far more wary of using infinite sets than modern mathematicians. To date, rational trigonometry is largely unmentioned in mainstream mathematical literature.
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