Q4 of 28 Page 84

The bisectors of ∠ B and ∠ C of a Δ ABC meet at O.

Show that BOC = 90o +

Theorem 1:


The sum of all three angles is 180°.


Let the ∠ B and ∠ C be 2x and 2y respectively.



In Δ ABC


∠A + ∠B + ∠C = 180° (Angle Sum Property)


⇒ ∠ A + 2x + 2y = 180°


⇒ 2x + 2y = 180° - ∠A


⇒ 2(x + y) = 180° - ∠ A


⇒


⇒ …(1)


In Δ OBC


∠OBC + ∠ OCB + ∠ BOC = 180° (Angle Sum Property)


⇒ x + y + ∠ BOC = 180°


⇒


⇒


⇒


Hence Proved.


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