Find all 3 radii.

Question

Find all 3 radii.

anonymous · Answer

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AB=8  BC=13  AC=11

pfenn1 · Answer

The line AB is mad up of the radius of A and the radius of B.  Likewise for BC and AC.  So$$AB=r _{A}+r _{B}$$$$BC=r _{B}+r _{C}$$$$AC=r _{A}+r _{C}$$

anonymous · Answer

And then?

anonymous · Answer

(The hint was that it's a work around problem)

pfenn1 · Answer

You have three equations and three unknowns.  Do you know how to solve a system like this?

anonymous · Answer

nope

anonymous · Answer

I'll understand if you just show all the work ;)

pfenn1 · Answer

Okay.  Let's rearrange the 3rd equation$$r _{C}=11-r _{A}$$Let's plug this into the second equation to get$$r _{B}+(11-r _{A})=13$$$$r _{B}-r _{A}=2$$ Now you can use this equation and the first equation to solve for r_B and r_A.
$$r _{A}+r _{B }=8$$

anonymous · Answer

Give me the final equation for the answer and the answer, please.

pfenn1 · Answer

You know$$r _{A}+r _{B}=8$$$$r _{B}-r _{A}=2$$If you add the 2 equations together you get$$2r _{B}=10$$You should be able to handle it from here.