Given that AC and AE are common external tangents of circle G and circle D, FE = 15, GF = 3, and AG = 5, which is the length of AC?
can you explain the whole process so i know what to do on other questions like this?

Question

Given that AC and AE are common external tangents of circle G and circle D, FE = 15, GF = 3, and AG = 5, which is the length of AC? 
can you explain the whole process so i know what to do on other questions like this?

anonymous · Answer

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anonymous · Answer

Per construction we have AB=AF BC=FE and AC=AE
Point of tangency are detremining square angle with rdaius of both circle, consequently we have 4 rectangle triangle. 
We can apply pythagore on AFG 
Then $$AG ^{2}-GF ^{2}=AF ^{2}$$
$$AF=\sqrt{AF ^{2}}$$

Given
AF=4 AND AC=19