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A Level Maths Circle Geometry help

I have this question that I am stuck on.

The points A (1,3) B(1,7) and C(7,7) lie on the circle (x-4)^2+(y-5)^2 = 13 By considering the gradients of AB and BC show that AC is a diameter of the circle.

I would appreciate any help thank you.

Reply 1

3pointonefour

Have you tried sketching it?

Reply 2

epic08

Original post by 3pointonefour

Have you tried sketching it?

Yes, I sketched it out but I am stuck with how you would prove it. I am revising for an exam so I am doing textbook questions and because it's a "show that" it doesn't give an answer.

Reply 3

3pointonefour

What do you notice about the lines AB and BC?

Reply 4

Ã„ries

converse of angle in semicircle

Reply 5

epic08

Original post by 3pointonefour

What do you notice about the lines AB and BC?

I worked out the gradient of BC to be 0. I think the lines are the same so they are both diameters. But how would I prove that just because BC is a diameter AC is too?