Question

Which statement is valid when a circumscribed circle of an acute triangle is

Answer 1

There are two answers: Choice C, Choice D

Explanation:

For any acute triangle, the center of the circle is always inside the triangle.

For any right triangle, the center of the circle is the midpoint of the hypotenuse. The hypotenuse is the diameter of the circle.

For any obtuse triangle, the center of the circle is outside the triangle.

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Let's look at the answer choices more closely

A. False. This is only true if we have a right triangle as mentioned earlier.

B. False. This describes an inscribed circle.

C. True. As stated earlier.

D. True. This is based on how the circumscribed triangle is defined. It is set up to be the circle that goes through all three vertex points of a triangle. In other words, it is the smallest circle to completely enclose the given triangle.