In the command below, type the new coordinates of the points. Evaluate the notebook.
In[]:=
Case3Taylor[tri={{5,5},{7,12},{9,-4}}]
The circumferences of the Taylor's case 3 proporties:
{Center1,Radius1,Equation1}
{Center2,Radius2,Equation2}
{Center3,Radius3,Equation3}

1465440
118243
,
1209655
236486
,
3025
65
5141
46
,
14790525
118243
-
2930880x
118243
+
2
x
-
1209655y
118243
+
2
y
0

1263233
79235
,
494466
79235
,
1458
97
3445
23
,
14260091
79235
-
2526466x
79235
+
2
x
-
988932y
79235
+
2
y
0

2443007
145015
,
641564
145015
,
2888
53
6305
23
,
24775159
145015
-
4886014x
145015
+
2
x
-
1283128y
145015
+
2
y
0
Out[]=
Circumference 1
Circumference 2
Circumference 3
Heights and their feet
Perpendiculars that pass through the feet of heights and their feet