Question

question #3
select all of the statements that are not true about circles.
a the circumference is about 2 times the diameter.
b the radius is half of the diameter.
c the radius divides a circle in half.
d the diameter is half of the radius.
e a chord must go through the center of a circle.
f the diameter is a chord.

Explanation:

Step1: Analyze Statement A

The formula for the circumference of a circle is \( C = \pi d \), where \( \pi \approx 3.14 \), so the circumference is about 3.14 times the diameter, not 2 times. So A is not true.

Step2: Analyze Statement B

By definition, the radius \( r \) of a circle is half of the diameter \( d \), i.e., \( r=\frac{d}{2} \). So B is true.

Step3: Analyze Statement C

A radius is a line segment from the center to the circumference. To divide a circle in half, we need a diameter (a line segment passing through the center with endpoints on the circle) or a straight line passing through the center. A single radius does not divide the circle in half. So C is not true.

Step4: Analyze Statement D

The diameter \( d = 2r \), so the diameter is twice the radius, not half. So D is not true.

Step5: Analyze Statement E

A chord is a line segment with both endpoints on the circle. A diameter is a chord that passes through the center, but not all chords pass through the center. So E is not true.

Step6: Analyze Statement F

A diameter is a chord (since it has endpoints on the circle and passes through the center), so F is true.

Answer:

A. The circumference is about 2 times the diameter,
C. The radius divides a circle in half,
D. The diameter is half of the radius,
E. A chord must go through the center of a circle