Question

question 8 of 10 what can be said about the relationship between triangles and circles? check all that apply. a. many circles can be inscribed in a given triangle, but they all have centers equal to the in - center. b. exactly one triangle can be inscribed in a given circle. c. many triangular shapes can be inscribed in a given circle. d. exactly one circle can be circumscribed about a given triangle.

Explanation:

• For option A: In a given triangle, only one incircle can be inscribed and its center is the in - center, so A is false.
• For option B: Many different triangles can be inscribed in a given circle, so B is false.
• For option C: Since the angles and side - lengths of a triangle inscribed in a circle can vary, many triangular shapes can be inscribed in a given circle.
• For option D: Given a triangle, there is exactly one circle (circum - circle) that can be circumscribed about it.

Answer:

C. Many triangular shapes can be inscribed in a given circle.
D. Exactly one circle can be circumscribed about a given triangle.