MathDB

On the plane, given an angle

xOy

M

be a mobile point on ray

Ox

and

N

a mobile point on ray

Oy

. Let

d

be the external angle bisector of angle

xOy

and

I

be the intersection of

d

with the perpendicular bisector of

MN

. Let

P

Q

be two points lie on

d

such that IP \equal{} IQ \equal{} IM \equal{} IN, and let

K

the intersection of

MQ

and

NP

1.

Prove that

K

always lie on a fixed line.

2.

Let

d_1

line perpendicular to

IM

M

and

d_2

line perpendicular to

IN

N

. Assume that there exist the intersections

E

F

d_1

d_2

from

d

. Prove that

EN

FM

and

OK

are concurrent.

Problem Statement