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In the given figure if O is the center o...

In the given figure if O is the center of the cricle then the vlaue of `angle POR` is

A

`20^(@)`

B

`40^(@)`

C

`60^(@)`

D

`80^(@)`

Text Solution

Verified by Experts

The correct Answer is:
C
In the given figure, `angle POQ=10^(@), angleORQ=40^(@)`
`:. OP= OQ[ :.` radii of same circle]
`:. angleOQP= angle OPQ=10^(@)` (Give )
Again, OQ=OR ( `:.`radii of same circle)
Now, `angleOQR= angleORQ=40^(@)` (Given)
Now, `angle PQR= angle OQR - angle OQP` [ accroding to the figure]
`=40^(@)-10^(@)=30^(@) [ :. angleOQR=40^(@) and angleOQR=10^(@)]`
Then the angle is circle produed by the are `overset (frown)(PR)= anglePQR=30^(@)`
and the central angle =`anglePQR`
`:. anglePOR=2 anglePQR`[ by theoem-34]
`=2xx30^(@) [ :. anglePQR=30^(@)]`
`=60^(@)`
`:. (c)` is correct
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