Question

If I is the incentre of triangle ABC, then angle BIC is equal to
(A) 1/2 A
(B) 90° + 1/2
(C) 90° – 1/2
(D) A

Answer 1

Step-by-step EXPLANATION

• angle BlC equals to 180 -(angle IBC + angle IBC)
• 180 - 1/2 (B+C)
• 180 -1/2(180-A)
• 90+1/2A

HOPE ANSWER IS HELPFULL

Answer 2

The correct answer is ∠BIC = 90° + $\frac{1}{2}$∠BAC

Given:

I is the incentre of ΔABC

To Find:

∠BIC =  ?

Solution:

The point at which all the angle bisectors of a triangle meet is called the incentre of a triangle

Let us consider that the angles at vertices A, B, and C are 2a, 2b, and 2c respectively.

Therefore in ΔABC, we have

$\frac{1}{2}$∠BAC = a          ....................................(1)

∠A + ∠B+ ∠C = 180°, or

2a+2b+2c = 180

⇒ a =  90- (b +c)      ....................................(2)

In ΔBIC we have

∠BIC = 180-(b + c)  = 90 + 90- (b +c) = 90 + a        ...............from equation(2)

Hence,

∠BIC = 90 + $\frac{1}{2}$∠BAC

The correct answer is ∠BIC = 90° + $\frac{1}{2}$∠BAC

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