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Kvant 2021
M2648
M2648
Part of
Kvant 2021
Problems
(1)
Geometry with qual inradii
Source: Kvant Magazine No. 4 2021 M2648
3/9/2023
The triangle
A
B
C
ABC
A
BC
is given. Consider the point
C
′
C'{}
C
′
on the side
A
B
AB
A
B
such that the segment
C
C
′
CC'
C
C
′
divides the triangle into two triangles with equal radii of inscribed circles. Denote by
t
c
t_c
t
c
the length of the segment
C
C
′
CC'
C
C
′
. Similarly, we define
t
a
t_a
t
a
and
t
b
t_b
t
b
. Express the area of triangle
A
B
C
ABC
A
BC
in terms of
t
a
,
t
b
t_a,t_b
t
a
,
t
b
and
t
c
t_c
t
c
.Proposed by K. Mosevich
geometry
inradius
Kvant