Let $ABCD$ be a parallelogram with sides a and b $(a>b)$ and let $r=a/b$ the ratio of the two sides.
The two diagonals form 4 angles which are by two congruent. Let's call the acute angle φ and the obtuse θ. Find the maximum value that φ can take, in relation to r.
I have managed to find a relationship for the angles φ and θ, but they also contain the diagonals: $\cosφ = (D_1^2+D_2^2-4b^2)/2D_1D_2$ and $\cos θ = (D_1^2+D_2^2-4a^2)/2D_1D_2$ but I don't know how to get rid of the diagonals and somehow take into account the ratio a/b.