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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