Correct Answer - Option 2 : 13/2 cm
Given:
In ΔABC, AB = 5 cm, BC = 12 cm and AC = 13 cm
Formula Used:
Circumradius of a triangle(R) = abc/4Δ
Where, a, b and c are lengths of sides of triangle and Δ is area of triangle.
Calculation:
In ΔABC, AB = 5 cm, BC = 12 cm and AC = 13 cm
Now,
By Pythagoras theorem
(13)2 = (5)2 + (12)2
⇒ ΔABC is a right angled triangle
⇒ Area of ΔABC = ½ × base × height = ½ × 5 × 12 = 30 cm2
⇒ Circumradius of a triangle(R) = abc/4Δ
∴ R = (5 × 12 × 13) / (4 × 30) = 13/2 cm
Alternate Method:
For any right-angled triangle, Circumradius = 1/2 × Hypotenuse
∴ Circumradius = R = 1/2 × 13 = 13/2 cm
