MathDB

5

Part of 2005 Argentina National Olympiad

Problems(1)

computational, ratio AP/CP wanted , AB/BC=2/3, tangent to circle

Source: 2005 Argentina OMA L3 p5

6/16/2020
Let AMAM and ANAN be the lines tangent to a circle Γ\Gamma drawn from a point AA (M(M and NN belong to the circle). A line through AA cuts Γ\Gamma at BB and CC with BB between AA and CC, and ABBC=23\frac{AB}{BC} =\frac23. If PP is the intersection point of ABAB and MNMN, calculate APCP\frac{AP}{CP}.
ratiogeometryTangentscircle