Question

CD is tangent to the circle and segment AE is perpendicular to segment AC. If a radius of the circle measures 12 in., which is the vale of DF + AF?

Answer 1

I want to say that DF + AF = 18

Answer 2

well i saw trigonometrics logtime ago, but lets hope that u learn somthing if its bad. Here ir goes.

First the angle of the triangle above EFA is 30. If am correcto u can get it by some angles propierties.

Then cos(30) = adjacent/h so h = 12/square(3)/2 = 24/square(3)

But u want to know the oposite, and u got h.

So sen(30) = oposite/h so oposite =12/square(3)

So u know now the lenght of the oposite side of the triangle DCF wich is 12(1- 1/square(3))

So u know AF, and u need DF

sen(30) = 12(1- 1/square(3))/h so h = 24(1 - 1/square(3))

DF = h

U sum them and get 36(1-1/squeare(3))

square is squeare root. Hope it helps. Maybe its wrong, but i tried xD.