perplexus.info :: Shapes : Circle Line Length

Circle Line Length (Posted on 2016-04-07)

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 = 90^o, PQ = 6, QR = 2
Find OR

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Solution

| Comment 2 of 3 |

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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