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M is the midpoint of PQ and N is the midpoint of PR, and O is the intersection of QN and RM, as shown. If $QN \perp PR$, QN = 12, and $PR = 18$, then find OR.

 

 Oct 24, 2021
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Notice that QO:ON = 2:1, since a median is divided into that ratio. (Search this up if you do not know). Therefore, from the given information, we know that ON = 4. Then, we also know that NR = 18/2 = 9. Since ONR is a right triangle, we can use the pythaogorena theorem from here in order to get our final answer:

 

OR = sqrt(9^2 + 4^2) = sqrt(97)

 Oct 25, 2021

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