Here is a question
Anyone know how to solve this or any hints to get me started as I am stuck.
The diagram shows a triangle ABC with sides BC a and AC b The points D,E and F lie on the sides AC,AB and BC, respectively, so that CDEF is a rhombus with sides of length x.
Find a expression for x in terms of a and b
Whatever $\angle BCA$ is, by similarity of $\triangle BFE$ and $\triangle BCA$ we must have $$\frac{a-x}x=\frac ab$$ $$b(a-x)=ba-bx=ax$$ $$ab=(a+b)x$$ $$x=\frac{ab}{a+b}$$