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प्रश्न
The internal bisectors of the angles B and C of a triangle ABC meet at I. If ∠BIC = `(∠A)/2` + X, then X is equal to
पर्याय
60°
30°
90°
45°
MCQ
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उत्तर
90°
Explanation:
In ΔABC,
∠A + ∠B + ∠C = 180°
∴ ∠B + ∠C = 180° – ∠A
∴ `1/2` (∠B + ∠C) = 90° – `(∠A)/2`
In ΔBIC,
`(∠B)/2 + (∠C)/2 + ∠BIC` = 180°
∴ 90° – `(∠A)/2` + ∠BIC = 180°
⇒ ∠BIC = 180° – 90° + `(∠A)/2`
= 90° + `(∠A)/2`
∴ X = 90°
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Geometry (Entrance Exam)
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