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2020 Ukrainian Geometry Olympiad - April
1
1
Part of
2020 Ukrainian Geometry Olympiad - April
Problems
(1)
isosceles criterion, equal perpσ on bisectors (Ukr. Geom. Olympiad '20 VIII p1)
Source:
6/8/2020
In triangle
A
B
C
ABC
A
BC
, bisectors are drawn
A
A
1
AA_1
A
A
1
and
C
C
1
CC_1
C
C
1
. Prove that if the length of the perpendiculars drawn from the vertex
B
B
B
on lines
A
A
1
AA1
AA
1
and
C
C
1
CC_1
C
C
1
are equal, then
△
A
B
C
\vartriangle ABC
△
A
BC
is isosceles.
geometry
isosceles
angle bisector
perpendicular