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Given :
∠AOP = ∠POC take as 'X'
∠BOR = ∠ROC take as 'Y'
We have X + X + Y + Y = 180 (on line AB)
2X + 2Y = 180
2 (X+Y) = 180
X + Y = 90
∴ ∠POC + ∠ROC = 90
∴ ∠POR = 90
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