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O is the circumecentre of triangle ABC. ...

O is the circumecentre of triangle ABC. If `angleOAB=50^(@)`, ten the value of `angleACB` is

A

`50^(@)`

B

`100^(@)`

C

`40^(@)`

D

`80^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let us join O, B
Now, OA= OB (`:.` radii of same circle)
`:. angleOBA= angleOAB=50^(@)` (Given)
`:. angle AOB=180^(@)-( angleOBA+ angleOAB)=180^(@)-(50^(@)+50^(@))=180^(@)-100^(@)=80^(@)`
Now,the angle in circle produced by the are `overset (frown)(AB)= angleACB` and the central angle
`= angleAOB=80^(@)`
`:. angleACB=(1)/(2) angle AOB`[ by theore -3] `=(1)/(2)xx80^(@)=40^(@)`
`:. (c)` is correct
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