Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
1. Section 11.1
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Exercise 10 Page 602

Practice makes perfect
a Examining the diagram, we notice that AB and CD are both the intercepted arc of the same central angle ∠ CPD. This must mean they have the same angle measure, so they are similar.
In order to transform AB onto CD we can use a dilation with a center at P. Check it by moving point A to point C on the diagram below.
b As discussed in Part A, AB and CD are both the intercepted arc of the same central angle. This means they have the same angle measure. However, regarding length, the circle that makes CD has a greater radius than the circle that makes AB. Therefore, it must be that CD>AB.
c Let's add the given values to the diagram.
To calculate the length of CD, we have to determine the circumference of a circle with a radius of 14 and multiply with the quotient of the 60^(∘) central angle and 360^(∘).

CD=2π( 14) 60^(∘)/360^(∘)≈ 14.66 units