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Question
If I is the incentre of triangle ABC and AI when produced meets the cicrumcircle of triangle ABC in points D. f ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠BIC.
Solution
Join DB and DC , IB and IC ,
∠ BAC = 66° , ∠ ABC = 80° , I is the incentre of the Δ ABC,
∠BAC = 66° and ∠ABC = 80°
In ∠ABC, ∠ACB = 180° - (∠ABC + ∠BAC)
⇒ ∠ACB = 180° - (80° + 66°)
⇒ ∠ACB = 180° - (156°)
⇒ ∠ACB = 34°
Since IC bisects the ∠C
∴ ∠ ICB = `1/2` ∠C = `1/2xx 34° = 17° `
Now in IBC
∠ IBC + ∠ICB + ∠ BIC =180°
⇒ 40° +17° + ∠ BIC = 180°
⇒ 57° + ∠ BIC = 180°
⇒ ∠ BIC = 180° - 57°
⇒ ∠ BIC = 123°
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