Multiple choice

A triangle ABC with sides AB = 15 cm, BC = 9 cm, CA = 12 cm is inscribed in a circle. What is the radius of the circle?

  1. 4.5 cm

  2. 6 cm

  3. 7.5 cm

  4. 15 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sides 9, 12, 15 form a right-angled triangle because 9^2 + 12^2 = 81 + 144 = 225 = 15^2. For a right triangle inscribed in a circle, the hypotenuse is the diameter. The radius is 15 / 2 = 7.5 cm.

AI explanation

The sides 9 cm, 12 cm and 15 cm form a Pythagorean triplet (9^2 + 12^2 = 15^2), so triangle ABC is right-angled at B where the hypotenuse is AC. By Thales's theorem, the hypotenuse of a right triangle inscribed in a circle acts as the diameter. The diameter is 15 cm, so the radius is 15 / 2 = 7.5 cm. The result is 7.5 cm.

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