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Turkey Contests
Turkey Team Selection Test
2020 Turkey Team Selection Test
2
2
Part of
2020 Turkey Team Selection Test
Problems
(1)
Tangential quadrilaterals
Source: 2020 Turkey TST P2
3/14/2020
A
1
A
2
A
3
A
4
A_1A_2A_3A_4
A
1
A
2
A
3
A
4
is a tangential quadrilateral with perimeter
p
1
p_1
p
1
and sum of the diagonals
k
1
k_1
k
1
.
B
1
B
2
B
3
B
4
B_1B_2B_3B_4
B
1
B
2
B
3
B
4
is a tangential quadrilateral with perimeter
p
2
p_2
p
2
and sum of the diagonals
k
2
k_2
k
2
.Prove that
A
1
A
2
A
3
A
4
A_1A_2A_3A_4
A
1
A
2
A
3
A
4
and
B
1
B
2
B
3
B
4
B_1B_2B_3B_4
B
1
B
2
B
3
B
4
are congruent squares if
p
1
2
+
p
2
2
=
(
k
1
+
k
2
)
2
p_1^2+p_2^2=(k_1+k_2)^2
p
1
2
+
p
2
2
=
(
k
1
+
k
2
)
2
geometry
perimeter