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If O is  the circumcentre of triangle ABC & as OD perpendicular to BC.
PROVE THAT :ANG.(BOD)=(BAC0 

Asked by aninadathoorsridharan 25th February 2016, 6:03 PM
Answered by Expert
Answer:

begin mathsize 14px style In space increment BOD space and space increment ODC comma Side space OD space common space to space both space the space triangles comma angle BDO space equals space angle CDO space space... space left parenthesis because OD perpendicular BC right parenthesis The space circumcentre space of space triangle space is space equidistant space from space the space vertices space of space the space triangle therefore BO space equals space CO space space... left parenthesis Radii space of space the space same space triangle right parenthesis space therefore increment BOD space approximately equal to space increment ODC therefore angle BOD space equals space angle COD space space... left parenthesis 1 right parenthesis space left parenthesis Corresponding space angles space of space congruent space triangles right parenthesis angle BAC space equals 1 half angle BOC space space... open parentheses Angle space subtended space by space the space arc space at space the space centre space is space twice space the space angle space subtended space by space the space same space arc space at space any space point space on space the space circumference space the space close parentheses therefore angle BAC space equals 1 half open parentheses angle BOD space plus space angle COD close parentheses space space... open parentheses because angle BOC equals angle BOD space plus space angle COD close parentheses But space therefore angle BOD space equals space angle COD space space... left parenthesis 1 right parenthesis therefore angle BAC space equals angle BOD  end style

 

 

Answered by Expert 25th February 2016, 7:09 PM
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