In a circle with centre O, BC is a chord. Points D and A are on the circle, on the opposite side of BC, such that ∠DBC = 28º and BD = DC. What is the measure of ∠BOC?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 112º
Concept
Angle formed by the arc is double the angle formed by the arc on the perimeter
Application
In ΔPBC,
∠PBC + ∠PCB + ∠BPC = 180°
Since BP = PC
∠PBC = ∠PCB = 28°
28° + 28° + ∠BPC = 180°
56° + ∠BPC = 180°
∠BPC = 180° – 56°
∠BPC = 124°
Angle formed by the arc is double the angle formed by the arc on the perimeter
∠BOC = 2 x 124° = 248°
Complete angle = 360°
Inverse of ∠BOC = 360° - 248° = 112°