MathDB
Problems
Contests
National and Regional Contests
India Contests
India IMO Training Camp
2023 India IMO Training Camp
3
Hard triangle geo (impossible?)
Hard triangle geo (impossible?)
Source: India TST 2023 Day 3 P3
July 9, 2023
geometry
Problem Statement
In triangle
A
B
C
ABC
A
BC
, with orthocenter
H
H
H
and circumcircle
Γ
\Gamma
Γ
, the bisector of angle
B
A
C
BAC
B
A
C
meets
B
C
‾
\overline{BC}
BC
at
K
K
K
. Point
Q
Q
Q
lies on
Γ
\Gamma
Γ
such that
A
Q
‾
⊥
Q
K
‾
\overline{AQ} \perp \overline{QK}
A
Q
⊥
Q
K
. Circumcircle of
△
A
Q
H
\triangle AQH
△
A
Q
H
meets
A
C
‾
\overline{AC}
A
C
at
Y
Y
Y
and
A
B
‾
\overline{AB}
A
B
at
Z
Z
Z
. Let
B
Y
‾
\overline{BY}
B
Y
and
C
Z
‾
\overline{CZ}
CZ
meet at
T
T
T
. Prove that
T
H
‾
⊥
K
A
‾
\overline{TH} \perp \overline{KA}
T
H
⊥
K
A
Back to Problems
View on AoPS