In the diagram, circle A is tangent to circle C, and segment BE is tangent to circle A. The radius of circle A is 11 meters and the radius of circle C is 8 meters. Find the area of triangle ABE to the nearest square meter.

Answer 1

I must assume that A and B are the centres of your two circles for this to make sense.
Join AE, and you will have a right angles triangle AEB
with AE=11, AB = 19 , and BE = x
x^2 + 11^2 = 19^2
x^2 = 240
x = √240

so the area = (1/2) base x height
= (1/2)(√240)(11)
= 22√15 or appr 85.2