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Adygea Teachers' Geometry Olympiad
2022 Adygea Teachers' Geometry Olympiad
3
3
Part of
2022 Adygea Teachers' Geometry Olympiad
Problems
(1)
BP bisects AC, incircle (2022 Adygea Teachers' Geometry Olympiad p3)
Source:
2/28/2024
The incircle of triangle
A
B
C
ABC
A
BC
touches its sides at points
A
′
A'
A
′
,
B
′
B'
B
′
,
C
′
C'
C
′
.
I
I
I
is its center. Straight line
B
′
I
B'I
B
′
I
intersects segment
A
′
C
′
A'C'
A
′
C
′
at point
P
P
P
. Prove that straight line
B
P
BP
BP
passes through the midpoint of
A
C
AC
A
C
.
geometry
bisects segment
incircle