MathDB

2005.G6

Part of Cono Sur Shortlist - geometry

Problems(1)

2 tangents. a secant, a ratio segment given, a ratio segment wanted

Source: Cono Sur Shortlist 2005 G6

7/26/2019
Let AMAM and ANAN be the tangents to a circle Γ\Gamma drawn from a point AA (MM and NN lie on the circle). A line passing through AA cuts Γ\Gamma at BB and CC, with B between AA and CC such that AB:BC=2:3AB: BC = 2: 3. If PP is the intersection point of ABAB and MNMN, calculate the ratio AP:CPAP: CP .
ratioTangentscirclegeometry