Question

IF THE BISECTOR OF ANGLE B AND C OF A TRIANGLE ABC MEET AT THE POINT O. THEN PROVE THAT ANGLE BOC=90+1/2ANGLE A

Answer 1

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Answer 2

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ANSWER....

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Given :-

Bisector of angle B and C of a triangle meet at point O.

Prove :-

Angle BOC = 1/2angle A

Proof :-

In ∆ABC ,

Angle A + Angle B + Angle C = 180°

Angle B + Angle C = 180° - AngleA

1/2Angle B + 1/2AngleC = 180/2 - 1/2AngleA

1/2Angle B + 1/2Angle C = 90° - 1/2AngleA

In ∆BOC ,

Angle (OBC + OCB + BOC) = 180°

1/2Angle B + 1/2Angle C + BOC = 180°

90 - 1/2Angle A + Angle BOC = 180°

Angle BOC = 180° - (90 - 1/2AngleA)

Angle BOC = 180° - 90° + 1/2AngleA

Angle BOC = 90° + 1/2Angle A

- Proved -