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.

Answer 1

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°