+33 Two circles are externally tangent at T. The line AB is a common external tangent to the two circles, and P is the foot of the altitude from T to line AB. Find the length 
TP.
+129852 Let O be the center of the larger circle and let N be the center of the smaller circle
Extend BA and ON to meet at M
Let MN = 3 + x MT = 6 + x OM = 13 + x NA = 3 BO = 7
First relationship
MN / NA = MT / TP
NA / MN = TP / MT
3 / (3 + x) = TP / (6 + x)
TP = 3(6 + x) / (3 + x)
Second relationship
TP / MT = BO / OM
3 (6 + x) / (3 + x) 7
______________ = ________
(6 + x) (13 + x)
3 / ( 3 + x) = 7 / (13 + x)
3(13 + x) = 7(3 + x)
39 + 3x = 21 + 7x
18 = 4x
x = 18/4 = 9/2
TP = 3(6 + 9/2) / (3 + 9/2) = 21 / 5 = 4.2
CORRECTED !!!!
