Calculating radius using tangent point and center point

Question

I got 2 coordinates which are given to me, they can be random. One is a tangent point coordinate and the other is center point coordinate.

I would like to get the radius of the circle using these 2 points. How would I do that? Is there a formula or something I have forgotten about?

is the tangent point the intersection of the tangent and the circle? — Pete Langshaw, Sep 26 '17 at 22:34

score 0 · Accepted Answer · answered Sep 26 '17 at 22:58

0

Given the centre $(x_1,y_1)$ and a point on the circumference of the circle $(x_2,y_2)$ then using the general form of a circle in the Cartesian plane$$(x-x_1)^2+(y-y_1)^2=r^2$$ and calculating the radius using the distance formula $$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ we would get $$(x-x_1)^2+(y-y_1)^2=(x_2-x_1)^2+(y_2-y_1)^2$$ which can be expanded and simplified if required.

answered Sep 26 '17 at 22:58

Pete Langshaw

110

Thank you, that works, just needed the second formula and could calculate the radius which I needed – Melkyp Sep 26 '17 at 23:27

Calculating radius using tangent point and center point

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