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)

Thanks.