Maths-

General

Easy

Question

# In the figure, the sides AB and AC of are produced to P and Q respectively. The bisectors of and intersect at O. Prove that .

Hint:

### find that alternate interior angles are equal then the lines are parallel.

Using condition given conditions find relation between ∠C and ∠ ADC.

## The correct answer is: Hence proved

### In triangle ABC

(∠ABC + ∠ ACB )= 180 - ∠ A(sum of angles in triangle)

now , ∠CBP = ∠ A + ∠ ACB (exterior angle property)

so ,∠ CBO = ×∠ A + × ∠ ACB (OB is angular bisector)

similarly,

∠BCO = × ∠ A + × ∠ ABC

In triangle BOC,

∠BOC = 180 - ∠CBO - ∠BCO (sum of angles in a triangle)

∠ BOC = 180 - (∠CBO + ∠ BCO)

∠ BOC = 180 - (× ∠ A + × ∠ ABC + × ∠ A + × ∠ ACB)

∠ BOC = 180 - (∠A + × ∠ ABC + × ∠ ACB)

∠BOC = 180 - (∠A + 90 - × ∠A)

∠BOC = 90 - × ∠ A

Hence prove

similarly,

In triangle BOC,

Hence prove

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