Question

OD, OE and OF are perpendicular bisectors to the three sides of the triangle. What is the relationship between $m\angle BAC$ and $m\angle BOC$?

• A. $m\angle BAC={180}^{\circ }-m\angle BOC$
• B. $m\angle BOC={90}^{\circ }+\frac{1}{2}m\angle BAC$
• C. $m\angle BOC={90}^{\circ }+\frac{1}{2}m\angle BOC$
• D. $m\angle BOC=2m\angle BAC$

Answer 1

The correct option is D $m\angle BOC=2m\angle BAC$

As the point 'O' is formed by the $\perp$ bisectors to the three sides of the $\Delta$, so point 'O' is the circumcenter. This means that virtually, points A, B and C are on the circumference of the circle.
Thus m $\angle BOC=2m\angle BAC$ (Since, the angle subtended by an arc at the centre of the circle is twice the angle subtended at the circumference).