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Korea Contests
Korea Junior Mathematics Olympiad
2022 Korea Junior Math Olympiad
1
1
Part of
2022 Korea Junior Math Olympiad
Problems
(1)
An acute triangle which is not isosceles
Source: kjmo 2022 p1
10/29/2022
The inscribed circle of an acute triangle
A
B
C
ABC
A
BC
meets the segments
A
B
AB
A
B
and
B
C
BC
BC
at
D
D
D
and
E
E
E
respectively. Let
I
I
I
be the incenter of the triangle
A
B
C
ABC
A
BC
. Prove that the intersection of the line
A
I
AI
A
I
and
D
E
DE
D
E
is on the circle whose diameter is
A
C
AC
A
C
(passing through A, C).
geometry
incenter