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# Geometry help

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Hi there! I'm back with another problem. I apologize-- my class is getting more difficult and my homework is piling up. It would be a huge favor if someone could help me with this problem:

Let $k$ be a positive real number. The line $x + y = k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

I think I'm supposed to use desmos? (that is allowed in my course as long as it's helpful to the student).

So, before I submit my answer can someone tell me if the answer: $\boxed{2}$ is right? Thanks so much! I really appreciate it :)

Jun 26, 2021

#1
+320
+5

Hey there, Guest!

Yes, you're right, let me show you how:

The distance of the line x+y = k from the centre of the given circle is k/$$\sqrt{2}$$And the circle's radius is $$\sqrt{k}$$. Therefore the tangency is (k/$$\sqrt{2}$$) of which equals $$\sqrt{k}$$, which is equal to 2.

Hope this helped! :)

( ﾟдﾟ)つ Bye

Jun 26, 2021

#1
+320
+5

Hey there, Guest!

Yes, you're right, let me show you how:

The distance of the line x+y = k from the centre of the given circle is k/$$\sqrt{2}$$And the circle's radius is $$\sqrt{k}$$. Therefore the tangency is (k/$$\sqrt{2}$$) of which equals $$\sqrt{k}$$, which is equal to 2.

Hope this helped! :)

( ﾟдﾟ)つ Bye

TaliaArticula Jun 26, 2021