MathDB

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

Source: 2005 Argentina OMA L3 p5

June 16, 2020

ratiogeometryTangentscircle

Problem Statement

Let

AM

and

AN

be the lines tangent to a circle

\Gamma

drawn from a point

A

(M

and

N

belong to the circle). A line through

A

cuts

\Gamma

B

and

C

with

B

between

A

and

C

, and

\frac{AB}{BC} =\frac23

. If

P

is the intersection point of

AB

and

MN

, calculate

\frac{AP}{CP}