MathDB
Problems
Contests
National and Regional Contests
New Zealand Contests
Auckland Mathematical Olympiad
2023 Auckland Mathematical Olympiad
2
2
Part of
2023 Auckland Mathematical Olympiad
Problems
(1)
triangle by equal segments on triangles' extensions (2023 Auckland MO p2)
Source:
3/26/2024
Triangle
A
B
C
ABC
A
BC
of area
1
1
1
is given. Point
A
′
A'
A
′
lies on the extension of side
B
C
BC
BC
beyond point
C
C
C
with
B
C
=
C
A
′
BC = CA'
BC
=
C
A
′
. Point
B
′
B'
B
′
lies on extension of side
C
A
CA
C
A
beyond
A
A
A
and
C
A
=
A
B
′
CA = AB'
C
A
=
A
B
′
.
C
′
C'
C
′
lies on extension of
A
B
AB
A
B
beyond
B
B
B
with
A
B
=
B
C
′
AB = BC'
A
B
=
B
C
′
. Find the area of triangle
A
′
B
′
C
′
A'B'C'
A
′
B
′
C
′
.
geometry
areas