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2021-IMOC
G2
G2
Part of
2021-IMOC
Problems
(1)
Midline and tangent related geo, equal angles wanted
Source: IMOC 2021 G2
8/11/2021
Let the midline of
△
A
B
C
\triangle ABC
△
A
BC
parallel to
B
C
BC
BC
intersect the circumcircle
Γ
\Gamma
Γ
of
△
A
B
C
\triangle ABC
△
A
BC
at
P
P
P
,
Q
Q
Q
, and the tangent of
Γ
\Gamma
Γ
at
A
A
A
intersects
B
C
BC
BC
at
T
T
T
. Show that
∡
B
T
Q
=
∡
P
T
A
\measuredangle BTQ = \measuredangle PTA
∡
BTQ
=
∡
PT
A
.
geometry
circumcircle