perplexus.info :: Geometry : From Tangent to Circle

From Tangent to Circle (Posted on 2017-01-04)

The line Ax+By=C (with C nonzero) is tangent to some circle centered at the origin.

What is the radius of that circle in terms of A, B, and C?
What is the point of tangency in terms of A, B, and C?

No Solution Yet Submitted by Brian Smith

Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

re: solution for part 2; outline for part 1

| Comment 2 of 4 |

(In reply to solution for part 2; outline for part 1 by Charlie)

Given Charlie's start, the rest can be done in my head.

The point of tangency simplifies to

a*c / (a^2+b^2), b*c / (a^2+b^2)

The radius is therefore

sqrt(a^2+b^2)* c/(a^2+b^2)

= c/sqrt(a^2+b^2)

Edited on January 5, 2017, 8:26 am

Posted by Steve Herman on 2017-01-04 16:45:34

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