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In figure (not to scale), the points M, ...

In figure (not to scale), the points `M, R, N, S, Q` are concyclic. Find `/_PQR+/_OPR+/_NMS+/_OSN`. if `'O'` is the center of the circle.

Text Solution

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`2/_PQR=/_POR`
`OR=OP=Y`
`/_ORP` is an isosceles triangle
`/_OPR=(180^0-2theta)/2=90^0-theta`
`/_PQR+/_OPR=90^0-(1)`
`/_NMS+/_OSN=90^0`-(2)
adding equation 1 and 2
`/_PQR+/_OPR+/_NMS+/_OSN=180^0`.
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