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# Week 6, problem of the week.

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Hello, here's another problem of the week!

What is the shortest distance, in units, between the circles $$(x-9)^2 + (y-5)^2 = 6.25$$ and $$(x+6)^2 + (y+3)^2 = 49$$? Express your answer as a decimal to the nearest tenth.

Aug 31, 2018

### 1+0 Answers

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This is a bit tough, but here's my take!

The shortest distance between two circles, is: $$C_1C_2-r_1-r_2$$.

We have $$C_1$$ as (9,5) as we take out the negatives from (-9,-5), and the radius is 2.5.

And, we have $$C_2$$ as (-6,-3) as we add the negatives from (6,3), and the radius is 7.

Now, we use the distance formula! $$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ Plugging in the value we get,

$$\sqrt{(-6-9)^2+(-3-5)^2}=\sqrt{225+64}=\sqrt{289}=17$$. After this, we subtract both radii, to attain:

$$17-2.5-7=17-9.5=\boxed{7.5}$$.

Sep 1, 2018

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