Question

If I is the incentre of triangle ABC and AI when produced meets the cicrumcircle of triangle ABC in points D . if ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠IBC

Answer 1

Join DB and DC , IB and IC ,

∠ BAC = 66° , ∠ ABC = 80° , I is the incentre of the Δ ABC,

Since I is the incentre of ∆ABC, IB bisects ∠ABC

∴ ∠ IBC = `1/2`  ∠ABC = `1/2 xx 80° = 40° `