The circumcentre of the triangle ABC is O Prove that angle OBC+angle BAC=90 degree Please answer fast!!!!!! - Maths - Areas of Parallelograms and Triangles

Question

The circumcentre of the triangle ABC is O Prove that angle
OBC+angle BAC=90 degree Please answer fast!!!!!!

Somnath maths · Accepted Answer

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Given, O is the circumcenterConstruction: OC joined To prove:
∠OBC​+∠BAC = 900Proof:In ΔOBC OB = OC
[∵radii of same circle]∴ΔOBC is
isosceles∠OBC = ∠OCB ---1 [∵Angles opposite to equal
sides of an isosceles triangle]Again,∠BOC =2∠BAC ---2
[∵Angle at the center is twice the angle at the
circumference]In ΔOBC ∠OBC+∠OCB+∠BOC =1800
[∵Sum of angles of a triangle]=>2∠OBC + ∠BOC =1800
[∵By eqn 1]=>2∠OBC+2∠BAC=1800 [∵By eqn
2]=>∠OBC+∠BAC=18002=900=>∠OBC+∠BAC = 900Hence
proved

The circumcentre of the triangle ABC is O. Prove that angle OBC+angle BAC=90 degree. Please answer fast!!!!!!