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General

Easy

Question

# In △ABC, AD and are the bisectors of ∠A and ∠C respectively. AD and CE intersect at . If ∠ABC = 90^∘, then find ∠AOC.

Hint:

### As we know AD and CE are angular bisectors we find ∠OAC and ∠OCA in terms of ∠A and ∠C .We find the value of ∠AOC by using the sum of angles in the triangle is 180°

## The correct answer is: ∠AOC = 135°

###

Step 1:- find∠OAC and ∠OCA

In ABC ,

∠A+∠B+∠C = 180°(sum of angles in the triangle)

∠A+∠C = 180°- 90°

∠A+∠C = 90°

∠OAC = ½ ∠A (AD is angular bisector )

∠OCA = ½ ∠C (CE is angular bisector )

Step 2 :- Find ∠AOC

In AOC ,

∠AOC + ∠OAC + ∠OCA = 180°(sum of angles in the triangle)

∠AOC + ½ ∠A + ½ ∠C = 180°

∠AOC + ½ (∠A + ∠C) = 180° (Substitute ∠A+∠C = 90°)

∠AOC + ½ (90°) = 180° ∠AOC = 180°- 45° = 135°.

∴ ∠AOC = 135°

Step 1:- find∠OAC and ∠OCA

In ABC ,

Step 2 :- Find ∠AOC

In AOC ,

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