take p as 0 vector. and write other vertices as a,b,c
else use ptolemy inequality.
take the Euclidean plane with the complex plane. Let 𝑎,𝑏,𝑐 be the complex numbers corresponds to 𝐴,𝐵,𝐶 respectively.
T. Hayashi, Two theorems on complex number, Tôhoku Math. J., 4 (1913-1914), 68–70