MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
2019 India National OIympiad
5
5
Part of
2019 India National OIympiad
Problems
(1)
INMO 2019 P5
Source:
1/20/2019
Let
A
B
AB
A
B
be the diameter of a circle
Γ
\Gamma
Γ
and let
C
C
C
be a point on
Γ
\Gamma
Γ
different from
A
A
A
and
B
B
B
. Let
D
D
D
be the foot of perpendicular from
C
C
C
on to
A
B
AB
A
B
.Let
K
K
K
be a point on the segment
C
D
CD
C
D
such that
A
C
AC
A
C
is equal to the semi perimeter of
A
D
K
ADK
A
DK
.Show that the excircle of
A
D
K
ADK
A
DK
opposite
A
A
A
is tangent to
Γ
\Gamma
Γ
.
geometry
INMO
2019
P5