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.

Guest Jan 20, 2022

#1**+1 **

Well, first, triangleMOQ is the same as triangleNOR. We can use this similarity to say QO = RO. Aksi we know PR=15, and since N bisects PR, NR=7.5. We can write an equation which states OR^2=(7.5)^2+ON^2. Also, QO+ON=10 so RO+ON=10. Now that we know this, RO has to be more than 7.5 but less than 8.25. Try solving using that and you will have to do a bit more work.

ImDecentAtMath Jan 20, 2022

#3**0 **

Sorry to say, but you made a couple of mistakes:

1/ Triangles MOQ and NOR are not similar!!!

2/ QO and RO are not equal!!!

civonamzuk
Jan 20, 2022

#2**0 **

QN and RM are the medians of triangle PQR.

The ratio of QO to NO is 2:1

OR = sqrt[(QN/3)^{2} + (PR/2)^{2}]

civonamzuk Jan 20, 2022