MathDB

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

Source: Cono Sur Shortlist 2005 G6

July 26, 2019

ratioTangentscirclegeometry

Problem Statement

Let

AM

and

AN

be the tangents to a circle

\Gamma

drawn from a point

A

(

M

and

N

lie on the circle). A line passing through

A

cuts

\Gamma

B

and

C

, with B between

A

and

C

such that

AB: BC = 2: 3

. If

P

is the intersection point of

AB

and

MN

, calculate the ratio

AP: CP