△ABC is inscribed in a circle with centre O. If AB=35 cm, BC=12 cm and AC=37 cm, then what is the circumradius of the triangle?

Let's examine the side lengths of △ABC:
35
2
+12
2
=1225+144=1369
37
2
=1369

Since AB
2
+BC
2
=AC
2
, △ABC is a right-angled triangle with the hypotenuse being AC=37 cm.

For any right-angled triangle, the circumradius (R) is exactly half the length of its hypotenuse:

R=
2
Hypotenuse
​

R=
2
37
​
=18.5 cm