# 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.

Algebra ->  Algebra  -> Circles -> 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.      Log On

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 Geometry: Circles and their properties Solvers Lessons Answers archive Quiz In Depth

 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)   (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