Q. 173.7( 3 Votes )

In the given figure, BE is the bisector of B and CE is the bisector of ACD.

Prove that


Answer :

In triangle ABC we have,


A + B + C = 180


Let B = x and C = y then,


A + 2x + 2y = 180 (BE and CE are the bisector of angles B and C respectively.)


x + y + A = 180


A = 180 – (x + y) ………….(i)


Now, in triangle BEC we have,


B = x/2


C = y + ((180 – y) / 2)


= (180 + y) / 2


B + C + BEC = 180


x/2 + (180 + y) / 2 + BEC = 180


BEC = (180 – x – y) /2 ………..(ii)


From eq (i) and (ii) we get,


BEC = A/2


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