Tangent-secant Theorem
The tangent-secant theorem describes the relation of line segments created by a secant and a tangent line with the associated circle. This result is found as Proposition 36 in Book 3 of Euclid's ''Elements''. Given a secant ''g'' intersecting the circle at points G1 and G2 and a tangent ''t'' intersecting the circle at point ''T'' and given that ''g'' and ''t'' intersect at point ''P'', the following equation holds: :, PT, ^2=, PG_1, \cdot, PG_2, The tangent-secant theorem can be proven using similar triangles (see graphic). Like the intersecting chords theorem and the intersecting secants theorem The intersecting secant theorem or just secant theorem describes the relation of line segments created by two intersecting secants and the associated circle. For two lines ''AD'' and ''BC'' that intersect each other in ''P'' and some circle in '' ..., the tangent-secant theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a ...
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