MathDB
Problems
Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
2021 Canada National Olympiad
1
1
Part of
2021 Canada National Olympiad
Problems
(1)
Canada MO 2021 P1
Source:
3/12/2021
Let
A
B
C
D
ABCD
A
BC
D
be a trapezoid with
A
B
AB
A
B
parallel to
C
D
CD
C
D
,
∣
A
B
∣
>
∣
C
D
∣
|AB|>|CD|
∣
A
B
∣
>
∣
C
D
∣
, and equal edges
∣
A
D
∣
=
∣
B
C
∣
|AD|=|BC|
∣
A
D
∣
=
∣
BC
∣
. Let
I
I
I
be the center of the circle tangent to lines
A
B
AB
A
B
,
A
C
AC
A
C
and
B
D
BD
B
D
, where
A
A
A
and
I
I
I
are on opposite sides of
B
D
BD
B
D
. Let
J
J
J
be the center of the circle tangent to lines
C
D
CD
C
D
,
A
C
AC
A
C
and
B
D
BD
B
D
, where
D
D
D
and
J
J
J
are on opposite sides of
A
C
AC
A
C
. Prove that
∣
I
C
∣
=
∣
J
B
∣
|IC|=|JB|
∣
I
C
∣
=
∣
J
B
∣
.
geometry