Equation of Circles (Sec 3): Proven Method to Show PR is the Diameter of the Circle

In Equation of Circles, many upper Secondary students taking Additional Mathematics encounter questions that test their understanding of circles, diameters and how to apply midpoint and gradient concepts together. Here’s a classic example:

Question: In the diagram which is not drawn to scale, P, Q and R are points on the circle. Show that PR is the diameter of the circle and hence find the centre of the circle.

This type of question on Equation of Circles is commonly found in tests and exams, and often requires more than a quick glance at the diagram. Getting it right depends on understanding the relationships between the points and applying the right method.

For students who need homework help or just a second opinion on their working, having on-demand homework help makes a big difference. Scroll down to see how the solution unfolded step by step, in a real chat between student and mentor.

Real mentors, Real-time answers

Ben

Hello!!
Need help with part a?
A
In order to prove the PR is the diameter
First you can find the midpoint of PR
Find eqn of the linear function?
Then find the distance from the midpoint to Q
If the distance from midpoint to Q is the same as the midpoint to either P or R
Then we will be able to prove that it is the diameter
?
Ok I�ll try
The midpoint you should get (-8, 4)
The distance from midpoint to Q, you should get 10.

The distance from midpoint to R, it is also 10.

So you have proven that PR is the diameter of the circle ?
Yup I got it
Great!
Goodbye!

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