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I is the incentre of triangle ABC AI whe...

I is the incentre of `triangle ABC` AI when produced meets the circumcircle of `triangle ABC` in D.If `/_BAC=66^@` and `/_ACB=80^@` Calculate (i) `/_DBC` (ii) `/_IBC` (iii) `/_BID`

Text Solution

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`/_ A + /_B + /_C = 180^@`
`60^@ + /_B + 80^@ = 180^@`
`/_B = 180^@ - 80^@-66^@`
`= 34^@`
`/_DBC= /_DAC = (/_BAC)/2`
`/_DBC = 60^@/2 = 33^@`
`/_IBC = (/_B)/2 = 17^@`
As, `/_AIB = 180^@ - 17^@ - 33^@`
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