In the figure, PC is tangent to circle O at C. Prove that, if AD = DC, then DC is the mean proportional (geometric mean) of OD and PD.
Answers will vary.
Since AD = DC and O is the center of the circle, OP ? AC. OC ? PC (radius and tangent are
perpendicular). So ?OCP is a right triangle and is the altitude to the hypotenuse.Then CD
is the geometric mean of OD and PD.
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