Another Relation between the Areas of Triangles Associated with an Excircle

S

1

≈

7.04

S

2

≈

2.41

S

3

≈

4.62

S

2

+

S

3

≈

7.04

Let ABC be a triangle. Let D and E be the points of contact of the incircle of ABC with AB and AC. Let J be the excenter of the excircle opposite A and let G and F be the intersections of DJ and EJ with BC. Let

S

1

,

S

2

, and

S

3

be the areas of GJF, DBG, and ECF, respectively. Then

S

1

=

S

2

+

S

3

.