Eric Nicholas K's answer to LIME's Secondary 4 A Maths Malaysia question.
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When three points are on a circumcircle, it means that the three points lie on the circumference of the circle. The 'triangle' here is irrelevant.
A good theory to know is that the perpendicular bisector of any chord will definitely pass through the centre of the circle, where 'chord' refers to the line formed by joining any two points on the circumference (I believe you know what perpendicular bisector represents).
We use any two combinations of the three coordinates to form two perpendicular bisectors which meet at the centre of the circle and we can solve them simultaneously to find the centre of the circle.
The radius of the circle is then the distance between the straight line formed by joining the centre and any one of the points on the circumference of the circle.
When three points are on a circumcircle, it means that the three points lie on the circumference of the circle. The 'triangle' here is irrelevant.
A good theory to know is that the perpendicular bisector of any chord will definitely pass through the centre of the circle, where 'chord' refers to the line formed by joining any two points on the circumference (I believe you know what perpendicular bisector represents).
We use any two combinations of the three coordinates to form two perpendicular bisectors which meet at the centre of the circle and we can solve them simultaneously to find the centre of the circle.
The radius of the circle is then the distance between the straight line formed by joining the centre and any one of the points on the circumference of the circle.
Date Posted:
5 years ago
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