Question

A circle and an inscribed triangle are shown. The area of the circle shown is 36π square millimeters. Select the two statements that are true.

A. The triangle's area is half that of the circle.
B. The triangle has a side equal to the circle's diameter.
C. The circle's radius is 6 millimeters.
D. The circle's circumference is 36 millimeters.

Answer 1

The two true statements are Statement C and Statement D.

Step-by-step explanation:

In this question, we are given that the area of the circle is 36π square millimeters. Let's analyze the statements:

• Statement A: The triangle's area is half that of the circle. This statement is false. The area of the triangle cannot be determined without additional information.
• Statement B: The triangle has a side equal to the circle's diameter. This statement is false. The side of the inscribed triangle can vary and is not necessarily equal to the diameter of the circle.
• Statement C: The circle's radius is 6 millimeters. This statement is true. Since the area of the circle is 36π square millimeters, we can use the formula for the area of a circle to find the radius: A = πr², where A is the area and r is the radius. Substituting the given area, we have 36π = πr². Solving for r, we find r = 6 millimeters.
• Statement D: The circle's circumference is 36 millimeters. This statement is false. The circumference of a circle is calculated using the formula C = 2πr, where C is the circumference and r is the radius. Substituting the given radius, we have C = 2π(6) = 12π millimeters.

Therefore, the two true statements are Statement C and Statement D.