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Three points A, B and C lie on circle wi...

Three points A, B and C lie on circle with centre of O in such a way that AOCB is a parallelogeram.Find the value of `angle AOC`.

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We know that sum of any two adjacent angles of a parallelogram is `180^(@)`
`:. angle AOC+angleOAB= 180^(@) .......(1)`
Again, the central angle produced by the are `overset(frown)(AC)="reflex" angleAOC` and angle in circle `=angleABC`
`:.` by the theorme -34, reflex `angleAOC= 2 angleABC, or 360^(@)- angleAOC =2 angleAOC`.
`[ :. angleABC= angleAOC`, sinceangles of any parallelogram are equal.]
`or, 360^(@)= 3 angleAOC or, angle AOC=(360^(@))/(3) or, angleAOC=120^(@)`
`:. angle AOC=120^(@)`
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