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ANALYZING RELATIONSHIPS A $45^{\circ}$ arc in $\odot \mathrm{C}$ and a length of $\mathrm{PQ}$ to the length of RS is 2 to $1 .$ What is the ratio of $m \angle \mathrm{PCQ}$ to $\mathrm{mL} \mathrm{RCS}$ ?

$\frac{r_{1}}{r_{2}}=\frac{2}{3}$

Geometry

Chapter 11

Circumference, Area, and Volume

Section 1

Circumference and Arc Length

Area and Perimeter

Surface Area

Volume

Circles

Johns Hopkins University

Piedmont College

Utica College

Lectures

12:03

In mathematics, a theorem …

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In mathematics, the tangen…

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Find the length of an arc …

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04:00

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01:59

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01:32

you were doing problem number 32 and we know on this one they're the radius of Circle C is equal to our one. We also know that the radius of Circle P it's our two, the Ark major and Circle C. It's 45 degrees the ark major and Circle P is 30 degrees. Hey, we also know that the arc length the Ark links are equal. Okay, so we know that the arc length we can take 45 degrees over 360 degrees times to pie are one, and we can make that equal to 30 degrees over 360 degrees. Times to pie are too. Okay, so we can cancel out a couple of the same factors so we can get rid of that three sixties. We can get rid of the two pi leaving us with 45 degrees. 45 are one equals 30 are too. So we want to get the ratio of our one toe are too. So we need to get the R two over the other side and the numbers to the ah, the right side. So to do that, we can divide by 45 and that's gonna leave us with Our one equals 30. 45th times are too. Now we can divide by the art too. And that's gonna leave us with our one over. Our two equals 30 over 45. Let's reduce this down. And that's gonna leave us with our one over. Our two equals two thirds. So our ratio ISS of one are one toe are two is 2 to 3, so we can even leave it. Leave it as written to over three, or we can say 223

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