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Circle Line Length (Posted on 2016-04-07) Difficulty: 2 of 5
Each of the points P and Q lie on a circle with its center at O and having a radius of √50. Point R is inside the circle such that:
∠PQR = 90o, PQ = 6, QR = 2
Find OR

No Solution Yet Submitted by K Sengupta    
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Solution Solution Comment 2 of 2 |
First note that ∠POQ = 2*∠OQR
 
By the law of cosines
cos(POQ) = (50+50-36)/(2*50)=16/25

cos(POQ)=cos(2*OQR)=2cos(OQR)^2-1
cos(OQR)=sqrt(41/50)

By the law of cosines again
OR^2 = 50+4-2*sqrt(50)*2*cos(OQR)
OR^2 = 54-4sqrt(41)
OR = sqrt(54-4sqrt(41))
or about 5.328

  Posted by Jer on 2016-04-08 11:37:32
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