MathDB

Bosnia and Herzegovina TST 2004 Day 1 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 2004

September 17, 2018

circlecollineartouchinggeometry

Problem Statement

Circle

k

with center

O

is touched from inside by two circles in points

S

and

T,

respectively. Let those two circles intersect at points

M

and

N

, such that

N

is closer to line

ST

. Prove that

OM

and

MN

are perpendicular iff

S

N

and

T

are collinear