+1234 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 AB.
+399 Set the center of the small circle to be O1, and the center of the larger circle to be O2.
Draw a perpendicular line passing through O1, perpendicular to BO2, label the foot of the perpendicular point C.
ABCO1 is a rectangle, and so AB = CO1.
Also, CO2 = 4 - 1 = 3
Apply the pythagorean theorem, so (CO1)2=(O1O2)2-(CO2)2=25 - 9=16.
Therefore, CO1=AB=4.
