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  1. Problems
  2. /An arc AB of a circle with centre O makes an angle ∠ ACB = 36° at a point C on the major arc…
EasyMathematicsHigh School (9–10)GeneralGeometry › CirclesNumericalBoard Exam

An arc AB of a circle with centre O makes an angle ∠ ACB = 36° at a point C on the major arc…

StemPy LabContributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

An arc ABABAB of a circle with centre OOO makes an angle ∠ACB=36∘\angle ACB = 36^\circ∠ACB=36∘ at a point CCC on the major arc. Find ∠AOB\angle AOB∠AOB and ∠OAB\angle OAB∠OAB.

Check your answer

Work it out on paper, then type your number. The answer itself stays hidden.

Need a reminder? The key ideaShowHide

The angle at the centre is double the angle at any point on the remaining part of the circle. Angles in the same segment are equal. The angle in a semicircle is 90∘90^\circ90∘, and the hypotenuse of a right triangle is a diameter of the circle through its corners.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

Step 1. The centre. ∠AOB=2×36∘=72∘\angle AOB = 2 \times 36^\circ = 72^\circ∠AOB=2×36∘=72∘.

Step 2. The base angle. OA=OBOA = OBOA=OB, so ∠OAB=180∘−72∘2=54∘\angle OAB = \dfrac{180^\circ - 72^\circ}{2} = 54^\circ∠OAB=2180∘−72∘​=54∘.

Answer: ∠AOB=72∘\angle AOB = 72^\circ∠AOB=72∘ and ∠OAB=54∘\angle OAB = 54^\circ∠OAB=54∘.

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