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Random Geometry Problems from Ukrainian Contests
Ukrainian From Tasks to Tasks - geometry
2010.5
2010.5
Part of
Ukrainian From Tasks to Tasks - geometry
Problems
(1)
computational, in a right triangle (2010 From Tasks to Tasks, p5 Ukr )
Source:
5/2/2021
In a right triangle
A
B
C
ABC
A
BC
(
∠
C
=
9
0
o
\angle C = 90^o
∠
C
=
9
0
o
) it is known that
A
C
=
4
AC = 4
A
C
=
4
cm,
B
C
=
3
BC = 3
BC
=
3
cm. The points
A
1
,
B
1
A_1, B_1
A
1
,
B
1
and
C
1
C_1
C
1
are such that
A
A
1
∥
B
C
AA_1 \parallel BC
A
A
1
∥
BC
,
B
B
1
∥
A
1
C
BB_1\parallel A_1C
B
B
1
∥
A
1
C
,
C
C
1
∥
A
1
B
1
CC_1\parallel A_1B_1
C
C
1
∥
A
1
B
1
,
A
1
B
1
C
1
=
9
0
o
A_1B_1C_1= 90^o
A
1
B
1
C
1
=
9
0
o
,
A
1
B
1
=
1
A_1B_1= 1
A
1
B
1
=
1
cm. Find
B
1
C
1
B_1C_1
B
1
C
1
.
geometry
right triangle