Question

In the given figure, if O is the circumcentre of ∠ABC, then find the value of ∠OBC + ∠BAC.

Answer 1

Since, O is the circumcentre of   \[\bigtriangleup ABC\], So, O would be centre of the circle passing through points A, B and C. 

\[\angle ABC\]= 90°             (Angle in the semicircle is 90°.)

\[\Rightarrow \angle OAB + \angle OBC = 90°\]            .....(1)

As OA = OB    (Radii of the same circle)

\[\therefore \angle OAB = \angle OBA \left( \text{ Angle opposite to equal sides are equal } \right)\]

\[\text{ or } , \angle BAC = \angle OBA\]

\[\text{ From }  \left( 1 \right)\]

\[\angle BAC + \angle OBC = 90°\]