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HOW DO YOU SEE IT?Compare the circumference of $\odot \mathrm{P}$ to the length of DE. Explain your reasoning.

The radius of $C$ is therefore 2$r .$ The arc length $D E$ is subtended by astraight angle and so can be evaluated as: $\frac{180^{\circ}}{360^{\circ}} \times 2 \pi \times 2 r=2 \pi r .$ It cantherefore be seen that the arc length $D E$ is equal to the circumference ofthe circle $P .$

Geometry

Chapter 11

Circumference, Area, and Volume

Section 1

Circumference and Arc Length

Area and Perimeter

Surface Area

Volume

Circles

Johns Hopkins University

Missouri State University

Utica College

Lectures

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Okay, we're gonna do problem. 36. They have a circle with a diameter of d E. And this is circle C inside. That they have a smaller circle is a circle p. They want to know the comparison of the circumference of a circle p to the length of our d. So on circle P, let's just make the radius. Are so our circumference a circle p we'll be two pi r. Well, our radius of circle C then we'll be to our. So that means that our circumference of circle C will be two times pi times to our which would be the same thing as saying for our pie. Okay, so we know that the measure then of D E is 100 and 80 degrees because that's half of the circle. We know that he's the diameter. So to find the ark link, we'll take the 180 degrees and divide that by 3 60 multiply by the circumference which we found was for pi r. And this will turn out to be 1/2 times four pi r, which is gonna end up being two pi r and noticed that the circumference of point key equals two pi R So the arc length is the same arc length. Ah, Arc de e equals the circumference of point P Oh!

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