# angle at centre equal twice angle at circumference

Author:
lookang
students must be able to understand why ∠ at Centre = 2 times ∠ at Circumference. Proof: Let ∠AOC = 2a Let ∠BOC = 2b Then ∠AOB = 360° - 2a – 2b ∠ OCA = 90° – a (isosceles triangle) ∠BCO = 90° – b (isosceles triangle) Therefore, ∠ACB = (90° – a) + (90° – b) = 180° – a – b Hence, ∠AOB = 2∠ACB (∠ at Centre = 2 times ∠ at Circumference) Proven http://weelookang.blogspot.sg/2014/12/geogebra-angle-at-centre-equal-twice.html

## angle at centre equal twice angle at circumference

Steps: 1. Compare angles at the centre of a circle with angle touching the circumference. 2. vary the ∠ at Centre O for which it is acute less than 90 ° 3. write down the value of ∠ at Centre O and ∠ at Circumference point A 4. vary the ∠ at Centre O for which it is obtuse more than 90° and less than 180°. 5. do step 3 6. vary the ∠ at Centre O for which it is reflex more than 180°. 7. do step 3 Thinking: looking at the evidence of the table of recorded values, suggest a relationship between ∠ at Centre O and ∠ at Circumference point A. Conclusion: ∠ at Centre = 2 times ∠ at Circumference.