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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 is perpendicular PR, QN = 12, and PR = 14, then find OR.

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 is perpendicular PR QN 12 and PR 14 then find OR class=

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sqdancefan

Answer:

 OR = √65

Step-by-step explanation:

M and N are the midpoints of their respective sides, so O is the centroid of the triangle. That means ...

  ON = QN/3 = 12/3 = 4

By the Pythagorean theorem, ...

  OR² = NR² +ON²

  OR² = 7² +4² = 65

  OR = √65

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