Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
Chapter Test
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Exercise 1 Page 817

Consider using the Pythagorean Theorem.

8

Practice makes perfect

Let's begin with recalling that a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle. This means that we have a right triangle in our diagram.

Notice that the legs of our triangle have lengths of 24 and 32. Let's say the length of the hypotenuse is c. Now, using the Pythagorean Theorem, we can find the value of c.
24^2+ 32^2= c^2
Solve for c
576+1024=c^2
1600=c^2
40=c
c=40
Notice that, since c represents the side length, we considered only the positive case when taking a square root of c^2. Now let's notice that the hypotenuse of the triangle is made of two segments, one of the length of x and the other that is a radius of a circle.

Therefore, by the Segment Addition Postulate, we can find the value of x. 32+x=40 ⇕ x=8