WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

The Sum of the Square Roots of the Areas of Three Subtriangles

​
S
≈
54.45
S
1
≈
1.81
S
2
≈
5.23
S
3
≈
14.02
S
≈
7.38
S
1
+
S
2
+
S
3
≈
7.38
Let ABC be a triangle. Let A'A'', B'B'', and C'C'' be tangents to the incircle of ABC and parallel to BC, AC, and AB such that A'', B' are on AB, B'', C' are on BC, and C'', A' are on CA. Let
S
be the area of ABC and
S
1
,
S
2
, and
S
3
be the areas of AA'A'', BB'B'', and CC'C'' respectively. Then
S
=
S
1
+
S
2
+
S
3
.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.