WOLFRAM|DEMONSTRATIONS PROJECT

A Parallelogram Defined by the Centers of Four Incircles

​
D
H
OO
1
≈
4.25
O
2
O
3
≈
4.25
O
1
O
2
≈
6.13
OO
3
≈
6.13
slope(​
OO
1
​)
≈
33.03
slope(​
O
2
O
3
​)
≈
33.03
slope(​
O
1
O
2
​)
≈
-0.58
slope(​
OO
3
​)
≈
-0.58
Let ABC be a triangle. Let the line DEF be parallel to AC with D on AB and E on BC. Let the line FGH be parallel to AB with H on AC and G on BC. Let O,
O
1
,
O
2
, and
O
3
be the incircles of the triangles ABC, DBE, FEG, and CGH, respectively. Then O
O
1
O
2
O
3
is a parallelogram.