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Leya [2.2K]
2 years ago
9

What is the length of AB?

Mathematics
2 answers:
nasty-shy [4]2 years ago
6 0
R = 14.5

form a right triangle with the 10 as 1st side and r as the hypotenuse.
get the length of the other side using pythagorean.

c = sqrt(14.5^2 - 10^2)  = 10.5

The length from the center to point A = c = 10.5
AB = r - c = 14.5 - 10.5 = 4

length AB = 4

makkiz [27]2 years ago
3 0
The radius of the circle is given to be r = 14.5

Let the center be O. So OB is the radius = 14.5

We can draw a triangle as shown in the image below. We have a right angled triangle. We know the hypotenuse and the base, we need to find the perpendicular side. This can be done using the Pythagorean theorem.

So, we can write:

(14.5)^{2}=10^{2}+OA^{2} \\  \\ 
OA^{2}=110.25 \\  \\ 
OA=10.5

Thus, the measure of OA = 10.5

OB = OA + AB

14.5 = 10.5 + AB
⇒
AB = 4
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If LR = 12 and LP = 7, find PR. Explain.
sergiy2304 [10]

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  PR = 5 because LP + PR = LR according to the Segment Addition Postulate, and 7 + 5 = 12 using substitution

Step-by-step explanation:

The naming of the segments suggests that point P is between L and R, so that ...

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This corresponds to the last choice.

_____

<em>Comments on the alternate interpretation</em>

On the other hand, if point L is between P and R, then the segments are PL and LR. The Segment Addition Postulate would tell you that ...

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The Reflexive Property of Congruence would tell you that PL = LP. The Substitution Property would tell you LP can be substituted into this equation, making it ...

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and by the commutative property, ...

  LR + LP = PR.

Multiple properties of addition and congruence are involved with this interpretation, which more or less matches the third choice. That is, the simple explanation of answer choice 3, by itself, is insufficient to explain why the length of PR should be considered to be 19, not 5.

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Step-by-step explanation:

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