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I am reading Gelfand's Trigonometry. In one of the questions he asks: "We know from geometry that a circle may be drawn through the three vertices of any triangle. Find the radius of such a circle if the sides of the triangle are 6,8, and 10."

My first question is, I know that if the diameter of a circle is the hypotenuse of a triangle then that triangle is a right triangle. Does this imply that the hypotenuse of any right triangle inscribed within a circle must be the diameter?

If this is not the case then I'm at a loss on how to solve this problem.

Second question, I have searched around but cannot find solutions to this book is there a place to find the solutions.

My first question is, I know that if the diameter of a circle is the hypotenuse of a triangle then that triangle is a right triangle. Does this imply that the hypotenuse of any right triangle inscribed within a circle must be the diameter?

If this is not the case then I'm at a loss on how to solve this problem.

Second question, I have searched around but cannot find solutions to this book is there a place to find the solutions.

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