Theory NO. 3 : Geometry, tangents and angles in circle
The angle which arms contain chords or tangents of a circle is the half of the sum (if the verticle of the angle lies inside the circle or on it) or difference (if the verticle lies outside) of middle angles based on the curves, which set this angle.
The proof can be illustrated by following pictures which consider all the possibilities.
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Tags: angle, angles, arm, chord, circle, math, tangent