Koostame vektori AB ja seejärele leiame selle pikkuse:

$$AB = (-1; 2)$$ $$AB = \sqrt{(-1)^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5}$$

Leiame kolmnurga külje AC pikkuse:

$$AC = (4; 6)$$ $$AC = \sqrt{4^2 + 6^2} = \sqrt{16 + 36} = \sqrt{52}$$

Leiame vektorite AB ja AC vahelise nurga:

$$\cos{a} = \frac{AB \cdot AC}{|AB| \cdot |AC|}$$ $$\cos{a} = \frac{(-1 \cdot 4) + (2 \cdot 6)}{\sqrt{5} \cdot \sqrt{52}} = \frac{4}{\sqrt{65}}$$ $$a = \arccos{\frac{4}{\sqrt{65}}}$$

Leiame kolmnurga ABC pindala:

$$S = \frac{1}{2} \cdot |AB| \cdot |AC| \cdot \sin{a}$$ $$S = 7$$

Leiame külje BC pikkuse:

$$BC = |AC - AB| = \sqrt{25 + 16} = \sqrt{41}$$

Leiame punkti C koordinaadid:

$$C = A + AC = (-1 + 4; 3 + 6) = (3; 9)$$

Leiame ringi võrrandi, mille keskpunkt on C ja mis läbib punkti B:

$$BC = r$$ $$r = \sqrt{41}$$ $$(x - 3)^2 + (y - 9)^2 = 41$$