MathDB

Lines intersecting circles

Source: Kürschák 2015, problem 2

October 7, 2016

geometryangle bisector

Problem Statement

Consider a triangle

ABC

and a point

D

on its side

\overline{AB}

. Let

I

be a point inside

\triangle ABC

on the angle bisector of

ACB

. The second intersections of lines

AI

and

CI

with circle

ACD

are

P

and

Q

, respectively. Similarly, the second intersection of lines

BI

and

CI

with circle

BCD

are

R

and

S

, respectively. Show that if

P\neq Q

and

R\neq S

, then lines

AB

,

PQ

and

RS

pass through a point or are parallel.

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