Q1 of 24 Page 296

The bisectors of ∠B and ∠C of ΔABC intersect at the point I. Let us prove that ∠BIC = 90° +



Let ∠ABI = ∠CBI = x


And ∠ACI = ∠BCI = y


In Δ ABC, using angle sum property,


∠A + 2x + 2y = 180° ….(1)


In Δ BIC, using angle sum property,


∠I + x + y = 180° ….(2)


Divide (1) by 2


We get,



Subtract (3) from (2)



Or



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