Derive Bretschneider's formula, Brahmagupta's formula and Heron's formula in one memorable elegant proof.
I ask this question merely to see the creativity of the MSE community when it comes to proof writing. Other than that, simplicity and good presentation is what I'm in search for.
Have fun :D
You can prove Bretschneider’s formula, then by giving appropriate values to the variables in the formula, prove the other two For Brahmagupta, the angle in the formula becomes 90, thus making the cosine zero, and the latter part of the formula disappears For Heron, substitute d by zero