ZACUAABICE 29Theorem 64 4If from a point outside a circle, a tangent and a secant are drawn to the circle, then the tangent is the mean proportional between the secant and its external segment. oket Given: Tangent PT touching circle O at T, and secant PA inter- secting the circle at B Prove: PA : PT = PT : PB - PA PT 17 Proof. Develop in class. PT PB Corollary 64-1 The product of any secant from a fixed point outside the circle and its external segment is constant. The length of a tangent from that point is constant. Corollary 64-2 If two or more secants are drawn to a circle from a fixed point outside the circle, then the product of one secant and its external segment is equal to the product of any other secant and its exter- nal segment.

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