SOLUTION: The bisector of a vertical angle A of a triangle ABC meets the circumcircle of triangle ABC at D. Show that D is the mid point of arc BDC. Prove with a diagram.

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Question 26653: The bisector of a vertical angle A of a triangle ABC meets the circumcircle of
triangle ABC at D. Show that D is the mid point of arc BDC. Prove with a diagram.
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
DRAW A CIRCLE.INSCRIBE A TRIANGLE ABC IN IT.DRAW AD BISECTING ANGLE BAC AND MEETING THE CIRCLE AT D.SO IN THE 2 SEGMENTS OF THE CIRCLE..NAMELY ARC BD AND ARC DC WE HAVE,BOTH ARCS SUBTENDING EQUAL ANGLES AT A .SINCE ANGLE BAD=ANGLE DAC.
SO THE ARCS SHALL BE EQUAL IN LENGTH.SO ARC BD = ARC DC
SO D IS THE MID POINT OF ARC BDC