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.