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Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Seniors Round2 2010+ geometry
2021.11.3
2021.11.3
Part of
Kyiv City MO Seniors Round2 2010+ geometry
Problems
(1)
circle tangent to incircle, <BKA=45^o (2021 Kyiv City MO Round2 11.3)
Source:
2/15/2021
In the triangle
A
B
C
ABC
A
BC
, the altitude
B
H
BH
B
H
and the angle bisector
B
L
BL
B
L
are drawn, the inscribed circle
w
w
w
touches the side of the
A
C
AC
A
C
at the point
K
K
K
. It is known that
∠
B
K
A
=
4
5
o
\angle BKA = 45^o
∠
B
K
A
=
4
5
o
. Prove that the circle with diameter
H
L
HL
H
L
touches the circle
w
w
w
.(Anton Trygub)
geometry
tangent circles