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Proof: Angle between a tangent and a chord | Geometry (TX TEKS) | Khan Academy
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https://www.khanacademy.org/math/geometry-tx/x790e3ac3e338c450:relationships-of-circles-including-radian-measure-and-equations-of-circles/x790e3ac3e338c450:properties-of-chords/v/proof-angle-between-a-tangent-and-a-chord
Let's prove that the measure of the angle formed by the intersection of a tangent and a chord is half the measure of the intercepted arc. We'll construct an isosceles triangle and use the relationship between radii and tangents of a circle to convince ourselves that this is true for both the major and minor arcs formed.
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