Question

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

(a) m ∠BAC = 180° – m ∠BOC 

(b) m ∠BOC = 2m ∠BAC 

(c) m ∠BOC = 90° + \(\frac{1}{2}\) m ∠BAC

(d)  m ∠BOC = 90° + \(\frac{1}{2}\) m ∠BAC

Answer 1

(b) m ∠BOC = 2m ∠BAC 

O being the point of intersection of the perpendicular bisectors of the sides of ∆ABC, it is the circumcentre of ΔABC.