Question

A circle is drawn with a center at point C. A line segment, AB, is drawn representing a diameter of the circle.

Which is true about the distance on the arc from A to B through point D?

The distance on the arc between the two points is undefined.
The distance on the arc between the two points is 180°.
The distance on the arc between the two points is twice the radius of the circle.
The distance on the arc between the two points is twice the diameter of the circle.

Answer 1

The CORRECT answer is:

The distance on the arc between the two points is twice the radius of the circle.

Explanation:

Radius times Radius = Diameter (180 times 180 = 360)

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A whole circle would be 360°, but since it is splitting directly in half of the circle and is looking for half the distance, it would be 180°.

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To be sure:

`360/2=180\\2*180=360`

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If you was to go even further, such as distance for A to D, it would be 1/4 of 360 (1/4 of the circle) which would be 90° since half of 180 is 90. The same will go for the distance from B to D, it would also become 90°.

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Thinking outside the "circle" (**BOX), C to D will also be 90°. You can also see it if you connect A to C, and C to D which will make it a 90° angle.

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Overall, this kind of math is kind of like cutting pieces of pie with your friends. This math can be done easily, but can also lead to probabilities and circumference of a circle.

©CDJ