WOLFRAM|DEMONSTRATIONS PROJECT

A Relation between Incircles and Excircles

point M

x	≈	1.29	y	≈	0.90	z	≈	1.78
X	≈	2.36	Y	≈	1.31	Z	≈	4.77

x

×

y

×

Z

≈

5.53

X

×

Y

×

z

≈

5.53

Let ABC be a triangle and M be a point on BC. Let

x

,

y

, and

z

be the radii of the incircles of the triangles ACM, ABM, and ABC and let

X

,

Y

, and

Z

be the radii of the corresponding excircles tangent to BC. Then

xyZ=XYz

.