Everything you did was splendid!
Since isosceles: .
We case use the Law of Sines on
The acute triangle inscribes a circle. D, E, and F are the tangent points. It is given that: , , and AF=a (see picture).
Using and a, express the following:
(a) the length of EF.
(b) the length of DF.
Well, first thing I thought about is that the angle between a tangent and chord is equal to the subtended angle on the opposite side of the chord, hence and , and since the triangle is an isosceles triangle (tangents drawn from a point outside the circle are equal in length), as well. In addition, and (is that correct?)
Does what I did help in solving the question? And what am I supposed to do next? (I must use the sine/cosine formulas)