MathDB

15th ibmo - venezuela 2000/q2.

Source: Spanish Communities

April 15, 2006

projective geometrygeometry unsolvedgeometry

Problem Statement

Let

S_1

and

S_2

be two circumferences, with centers

O_1

and

O_2

respectively, and secants on

M

and

N

. The line

t

is the common tangent to

S_1

and

S_2

closer to

M

. The points

A

and

B

are the intersection points of

t

with

S_1

and

S_2

,

C

is the point such that

BC

is a diameter of

S_2

, and

D

the intersection point of the line

O_1O_2

with the perpendicular line to

AM

through

B

. Show that

M

,

D

and

C

are collinear.

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