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In a triangle abc the bisector of angle b and angle a intersect at o. Prove that angle boc=90+1/2 anlge

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Secondary SchoolMath 13+7 pts

Bisectors of angle b and angle c intersect at o. prove that angle boc = 90 + 1/2 angle a

Report by Cutefam6058 12.03.2018

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Suchitrasihag1

Suchitrasihag1 Ambitious

To prove angle BOC = 90°+1/2 angle a

Proof: In triangle ABC

angle a+ angle B + angle c = 180° ( by angle sum property)

angle a + 2angle OBC+ 2angle ocb =180°

2( angle OBC+ angle ocb) =180°-angle a

angle obc + angle ocb = 180°/2-angle a/2

angle obc + angle ocb = 90°- a/2

Now in triangle BOC

angle boc + angle obc + angle ocb = 180° ( by angle sum property)

angle boc = 180° - ( angle obc+ angle ocb)

angle boc = 180° - (90°-angle a/2)

angle boc = 180°-90°+angle a/2

angle boc = 90°+angle a/2

H.P.