Triangle ABC has sides AB = 13 cm, BC = 14 cm and CA = 15 cm. What is the radius of its circumscribed circle?

First find the area with Heron's formula: s = (13 + 14 + 15)/2 = 21, so Area = √(21 × 8 × 7 × 6) = √7056 = 84 cm².

Circumradius R = abc/(4 × Area) = (13 × 14 × 15)/(4 × 84) = 2730/336 = 65/8 cm (= 8.125 cm).

8 cm and 33/4 cm are close decoys; 15/2 would be half the longest side, which applies only to a right triangle (13-14-15 is acute).

Tip: The 13-14-15 triangle splits into 5-12-13 and 9-12-15 right triangles with common altitude 12 — area 84 is worth memorising.