# A rectangular triangle with legs 6 and 8 cm is inscribed in a circle. Find the circumference.

June 29, 2021 | education

| The hypotenuse of a right-angled triangle inscribed in a circle lies on the diameter of the circle.

We calculate the length of the hypotenuse of a triangle using the Pythagorean theorem:

√ (6² + 8²) = √ (36 + 64) = √100 = 10 (cm) – the length of the diameter of the circle.

The radius of the circle is equal to half the diameter, R = 10: 2 = 5 (cm).

The circumference is calculated by the formula C = 2пR.

Let’s calculate the length of this circle: C = 2 * п * 5 = 10п.

Answer: the circumference is 10п.

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