What can be said about the relationship between triangles and circles? choose all that apply.
a. exactly one triangle can be inscribed in a given circle.
b. many triangular shapes can be inscribed in a given circle.
c. many circles can be inscribed in a given triangle but they all have centers equal to the incenter.
d. exactly one circle can be circumscribed about a given triangle.

The correct answers are:

B) many triangular shapes can be inscribed in a given circle; and
D) exactly one circle can be circumscribed about a given triangle.

Explanation:

One of our geometric theorem states that for any 3 non-collinear points, exactly one circle can be drawn through it. This explains answer D; the non-collinear points would be the vertices of the triangle, and only one circle can be drawn through those points (circumscrbied about the triangle).

For B, we can have many triangles inscribed in a circle; the differences in the measures of the angles used will create the different triangles.