Example 2 : Equation of a Circle given 3 points on the Circumference : ExamSolutions

This is the second video on finding the equation of a circle given three points on the circumference. You should be familiar with the method as shown in the first video. To see the maths revision guide on this go to ExamSolutions at http://www.examsolutions.co.uk/maths-tutorials/Core-maths/coordinate-geometry...

Category:

Education

Tags:

• A-level
• maths
• coordinate
• geometry
• equation
• circle
• Circumference
• ExamSolutions
• Exam
• Solutions

[64adamw64]

How am I meant to find the centre of a circle given only 2 points on the circle (a chord) and a tangent??

[ExamSolutions]

@64adamw64 Find out where the normal to the tangent and the perpendicular bisector of the chord intersect. You will need to establish the respective equations and solve simultaneously.

[tehemor]

Will the point of intersection of the perpendicular bisectors always be the centre point or is it just this specific example?

I'm pretty sure it is 'cause when I visualise it in my head it seems to be so but I don't know for sure...

Thanks for the videos, they're very helpful.

EMZ=]

[ExamSolutions]

@tehemor Yes

[MilitaryMan006]

how can you do a neat construction of the circle during the exam without knowing the centre?

[ExamSolutions]

@MilitaryMan006 practice and guess work

[tomwann1]

thank you this helped me alot, appreciate this keep up the good work

[64adamw64]

@ExamSolutions ok thanks :)

[MilitaryMan006]

another question, if you dont have a vertical chord can you still find the midpoint of the chord and perpendicular gradient and work it out via simultaneous equation?

[ExamSolutions]

@Goodfellow7 I would think so. I would encourage you to work it out algebraically. Suppose the real answer was (1.1, -2.1) or very close to your answer. Do you think you would have been able to spot this?