The cosine rule: proof without words

You use the Intersecting Chords Theorem.

If the triangle is a different shape, then its top vertex will be outside the circle. But the proof can be adapted. You just need the Intersecting Secants Theorem in place of the Intersecting Chords Theorem.

The proof is due to Sidney H. Kung (in the Mathematical Magazine of the Mathematical Association of America, December 1990).