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In the diagram above O is the center of the circle. If <TUR is 50ᵒ, find the value of <TOR.
- A. 40ᵒ
- B. 130ᵒ
- C. 100ᵒ
- D. 50ᵒ
There is a rule in circle geometry which states that angle at the center is twice the angle at the circumference provided the two angles are based on a common chord.
In the diagram above, <TOR and <TUR are based on the same chord TR, therefore;
<TOR = 2 <TUR = 2 × 50 = 100
Now for the right answer to the above question:
- Option A is incorrect.
- Option B is incorrect.
- C is correct.
- D is not the correct answer.
You may please note these/this:
- Angle at the center of a circle is twice the angle at any point on the circumference provided the two angles are based on the same chord.
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/ culled from 2015 JAMB-UTME mathematics past question 43 /