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In the given figure, O is the centre of ...

In the given figure, O is the centre of the circle. If `BD=DC` and `angleDBC=30^@`, find the measure of `angleBAC` and `angleBOC`.

Text Solution

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As `BD = DC`,
`:. /_DCB = /_DBC = 30^@`
`:. /_BDC = 180^@-/_DCB-/_DBC = 120^@`
Now, `ABDC` is a cyclic quadrilateral.
`:. /_BDC+/_BAC = 180^@`
`=>/_BAC = 180^@ - 120^@ = 60^@`
We know, angle subteded at the center by a chord is double than that of angle subtended at any point on the circle.
`/_BOC = 2/_BAC = 2**60^@=120^@`
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