An arc AB of a circle with centre O makes an angle ∠ ACB = 36° at a point C on the major arc…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
An arc of a circle with centre makes an angle at a point on the major arc. Find and .
Need a reminder? The key ideaShow
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 , 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. .
Step 2. The base angle. , so .
Answer: and .
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