Question

bisector of angles B and C of a triangle ABC intersect each other at point O prove that angle BOC is equal to 90 degree + half angle A​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given:-A traingle ABC in which BO and CO are the bisectors of <B and <C respectively

To prove:-<BOC=(90°+1/2<A)

Proof:-

We know that the sum of three angled of a triangle is 180°

<A+<B+<C=180°

1/2<A+1/2<B+1/2<C=90°

1/2<A+<OBC+<OCB=90°

<OBC+<OCB=(90°-1/2<A)

Now,in traingle ABC

<OBC+<OCB+<BOC=180°

(90°-1/2<A)+<BOC=180°

<BOC=180°-(90°-1/2<A)

=(90°+1/2<A)

Hence,<BOC=(90°+1/2<A)