Question

If the bisector of angles angleB and angleC of triangle ABC meet at a point O, then prove that angleBOC=90 degree +1/2 angleA

Answer 1

in a triangle ABC,we have: <A+<B+<C=180' (sum of the angle of triangle) © 1/2<A + 1/2<B + 1/2<C = 90'
® 1/2<A + <1 + <2 = 90' ©<1+<2=90-1/2<A Now,in triangle OBC,we have: ®<1+<2+<BOC=180 (sum of angle of a triangle) ©(90-1/2<A)+<BOC =180 (USING 1) ®<BOC=90+1/2<A 0 PROVED