The Feuerbach theorem and cyclography in universal geometry - Beare, William (Array, 2020)
We have another look at the Feuerbach theorem with a view to extending it in an oriented way to finite fields using the purely algebraic approach of rational trigonometry and universal geometry. Our approach starts with the tangent lines to three rational points on the unit circle, and all subsequent formulas involve the three parameters that define them. Tangency of incircles is treated in the oriented setting via a simplified form of cyclography. Some interesting features of the finite field case are discussed.