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AC tangent to (ABD), tangent and secant from the same point

Source: China Northern MO 2011 p6 CNMO

October 28, 2022
geometrytangent

Problem Statement

As shown in figure, from a point PP exterior of circle ⊙O\odot O, we draw tangent PAPA and the secant PBCPBC. Let AD⊥POAD \perp PO Prove that ACAC is tangent to the circumcircle of △ABD\vartriangle ABD. https://cdn.artofproblemsolving.com/attachments/a/f/32da6d4626bb3592cec19a4cf0202121ba64db.png
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