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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°


Team Careers360 22nd Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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