Question : A circle is circumscribing a triangle whose sides are 30 cm, 40 cm, and 50 cm. Find the circumference of the circle.
Option 1: $75 \pi$ cm
Option 2: $25 \pi$ cm
Option 3: $100 \pi$ cm
Option 4: $50 \pi$ cm
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Correct Answer: $50 \pi$ cm
Solution :
Given, the sides of the triangle are 30 cm, 40 cm, and 50 cm.
30 cm, 40 cm, and 50 cm form a pythagorean triplet.
In a right triangle, the circumradius (radius of the circle circumscribing the triangle) is half the length of the hypotenuse.
50 cm is the length of the hypotenuse of the triangle.
So, Circumradius, $r$ = 25 cm
Circumference of the circle = $2\pi r = 50\pi$ cm
Hence, the correct answer is $50 \pi$ cm.
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