If I have r as an inradius of a triangle and ra, rb, rc are the three radii of the 3 excircles of that triangle how can I show that:

1/ra+1/rb+1/rc=1/r?

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- Mar 2nd 2010, 04:39 AM #1

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- Mar 2nd 2010, 05:24 AM #2
Start here, with the formulas $\displaystyle r = A/s$, $\displaystyle r_a = A/(s-a)$, $\displaystyle r_b = A/(s-b)$, $\displaystyle r_c = A/(s-c)$, where A is the area of the triangle and $\displaystyle s = \tfrac12(a+b+c)$.

- Mar 2nd 2010, 08:20 AM #3

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- Oct 2009
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- Mar 2nd 2010, 09:03 AM #4

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