SOLUTION: A circle passes through the vertices of a triangle with sides of length 3.3 cm, 5.6 cm and 6.5 cm. The radius of the circle, in cm, is A) 2.3 B) 3.2 C) 3.25 D) 3.85 e) 5.16

Question 1189798: A circle passes through the vertices of a triangle with sides of length 3.3 cm, 5.6 cm and 6.5 cm. The radius of the circle, in cm, is
A) 2.3 B) 3.2 C) 3.25 D) 3.85 e) 5.16
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Use the pythagorean theorem converse to find that
a^2 + b^2 = c^2
(3.3)^2+(5.6)^2 = (6.5)^2
is a true equation. Both sides simplify to 42.25

Therefore, this is a right triangle.

For any right triangle, the circumscribed circle (aka circumcircle) has the hypotenuse as a diameter.
The radius is half the diameter, so c/2 = (6.5)/2 = 3.25 is the radius of the circumcircle.

For more info, check out Thales Theorem.

Answer: C) 3.25

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