Q. 63.8( 12 Votes )

ABC is a triangle. The bisector of the exterior angle at B and the bisector of C intersect each other at D. Prove that D = 1/2A.

Answer :



Exterior B = (180o - B)

Exterior C = (180o - C)


In


A + B + C = 180o


(A + B + C) = 180o


(B + C) = 180o - A (i)


In


D + DBC + DCB = 180o


D + {180o - (180o - B) - B} + {180o - (180o - C) - C} = 180o


D + 360o – 90o – 90o – (B + C) = 180o


D + 180o – 90o - A = 180o


D = A


Hence, proved

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