Thread: Is this true for all tangents to a circle?

Well, I was testing somethings out to try and find a particular point that is a tangent to a circle and I decided to try this. I'm not too sure whether it's right or not.

I just want to know if this is true for all tangents to a circle?



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Excuse the terrible picture. I just drew it in a rush on MS Paint. I am hoping you can decipher it.

Originally Posted by StephenPoco

Well, I was testing somethings out to try and find a particular point that is a tangent to a circle and I decided to try this. I'm not too sure whether it's right or not.

I just want to know if this is true for all tangents to a circle?

Excuse the terrible picture. I just drew it in a rush on MS Paint. I am hoping you can decipher it.

You've found a very special case which is only true if

In general:
1. Use the indicated blue triangle to determine the slope of the tangent:



2. Use the triangle RCQ to determine the slope of the tangent:



Since and the 2nd equation becomes:



3. You now can use these 2 equations to get some additional results.