Question : Points D, E, and F all lie on the circumference of a circle with centre O. If angle DEF = 48°, then what is a possible value of angle DOF?
Option 1: 84°
Option 2: 96°
Option 3: 90°
Option 4: 48°
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Correct Answer: 96°
Solution : The points D, E, and F lie in a circle with centre O. $\angle$DEF = 48$^{\circ}$ The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle. According to the concept, 2$\angle$DEF = $\angle$DOF ⇒ 2(48$^{\circ}$) = $\angle$DOF ⇒ $\angle$DOF = 96$^{\circ}$ Hence, the correct answer is 96$^{\circ}$.
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