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If O is the circumcentre of a A B C and...

If `O` is the circumcentre of a ` A B C` and `O D_|_B C ,` prove that `/_B O D=/_adot`

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Given A`Delta ABC` whose circumcentre is O and OD `_|_BC`.
To Prove `/_ BOD = /_ A`.
CONSTRUCTION Join OB and OC
PROOF In the right `Delta s ` OBD and OCD , we have
OB `=` OC [ radii of he same circle ]
OD `=` OD [common]
`:. Delta OBD ~= Delta OCD` [ by RHS congruence ]
`implies /_BOD = /_ COD `[ c.p.c.t.]
`implies /_BOD = (1)/(2) /_ BOC `
`implies /_BOD = (1)/(2) /_ BOC`
`implies /_BOD = /_ A [ :' /_A = (1)/(2) /_ BOC ]`.
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