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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 to PR, QN = 10, and PR = 15, then find OR.

 

 Jan 22, 2021

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 #3
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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 to PR, QN = 10, and PR = 15, then find OR.

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By the median theorem ON = QN / 3 = 10/3

 

NR = PR / 2 = 7.5

 

OR = sqrt{( 10/3)2 + 7.52} = 8.207381501smiley

 Jan 22, 2021
 #1
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https://web2.0calc.com/questions/help-asap_51751

 Jan 22, 2021
 #2
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Note that NR  =15/2 = 7.5  PN

 

Draw a perpendicular   MS   to   PR

 

Then triangle  PMS  is  similar to triangle PQN

 

Then since MP is 1/2   of PQ  then  PS  =  1/2 of PN =  7.5/2=  15/4  = 3.75    

 

And triangle PMS  is similar to  triangle PQN

 

So

 

PS/ PN  =  MS/QN

3.75/ 7.5  =  MS /QN

1/2 = MS/10

MS = (1/2) 10  = 5

 

And triangle    RSM  is similar to triangle  RNO

 

RS =  3.75 + 7.5 = 11.25

 

So

 

MS / RS  =  ON / NR

5/11.25 =  ON / 7.5

 

(7.5)(5) / 11.25 =  ON    =   10/3

 

cool cool cool

 Jan 22, 2021
 #3
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+1
Best Answer

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 to PR, QN = 10, and PR = 15, then find OR.

-------------------------------------------------------------

By the median theorem ON = QN / 3 = 10/3

 

NR = PR / 2 = 7.5

 

OR = sqrt{( 10/3)2 + 7.52} = 8.207381501smiley

Guest Jan 22, 2021

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