WOLFRAM|DEMONSTRATIONS PROJECT

Tangents to an Excircle

​
BD
≈
1.07
CE
≈
0.51
DE
≈
1.48
2
BD×CE
≈
1.48
A circle drawn outside a triangle that is tangent to the extensions of two of its sides and to the third side is an excircle.
Let ABC be a triangle. Construct the excircle with center O opposite A. Let D and E be the points of intersection between the line perpendicular to AO and the extensions of AB and AC. Then
DE=2
BD×CE
.