In this chapter we will derive formula to calculate the value of angle formed by joining two angle bisector of triangle.

Consider above triangle ABC in which BO & CO are angle bisectors dividing ∠B & ∠C into two equal parts.

These angle bisectors meet at point O.

The angle formed by angle bisector is given as;

∠BOC = 90 + 1/2 ∠A

## Proof of angle bisector formula

In above triangle ABC, OB and OC are angle bisectors.

∠ 1 = ∠2

∠ 3 = ∠4

Applying angle sum property in triangle ABC.

∠A + ∠B + ∠C = 180

∠A + 2( ∠ 1) + 2( ∠3) = 180

2( ∠ 1) + 2( ∠3) = 180 – ∠A

∠1 + ∠3 = 90 – 1/2 ∠A

Now apply angle sum property in triangle OBC.

∠1 + ∠3 + ∠BOC = 180

90 – 1/2 ∠A + ∠BOC = 180

**∠BOC = 90 + 1/2 (∠A)**

Hence Proved.

Try to memorize the formula, as it would help you solve question fast.