△ ABC is a right-angled triangle with ∠ ABC = 90^° . If m(AB̅) = 28 cm, and m(BC̅) = 96 cm, find the area (in cm²) of the circumcircle of △ ABC . (Use π = 3.14. )

△ ABC is a right-angled triangle with ∠ ABC = 90^° . If…

$\triangle ABC$ is a right-angled triangle with $\angle ABC = 90^\circ$ . If $m(\overline {AB})$ = 28 cm, and $m(\overline {BC})$ = 96 cm, find the area (in cm²) of the circumcircle of $\triangle ABC$ . (Use $\pi = 3.14.$ )

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 7,850.

In a right-angled triangle, the hypotenuse is the diameter of the circumcircle.

So, AC² = AB² + BC²

⇒ AC² = 28² + 96² = 784 + 9216 = 10000

⇒ AC = √10000 = 100 cm

Radius (r) = AC/2 = 100/2 = 50 cm

Area of the circumcircle = πr² = 3.14 × (50)² = 7850 cm²

Therefore, the area of the circumcircle of triangle ABC is 7850 cm².

SSC CGL 2024 PYQ — Question 70