Triangle Dilation by Radius Distance

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I'm attempting to follow the accepted solution here:

However, I cannot seem to get $k$ to equal out to the correct scalar value.

In my use case I made up a triangle of the following 3 points ${(0,0),(921,0), (460.5,265)}$ and I want to reduce the radius by 25.

Here is what I have so far:

$a=\sqrt((921-460.5)^2+(0-265)^2)=531.305$

$b=\sqrt((0-460.5)^2+(0-265)^2)=531.305$

$c=\sqrt((0-921)^2+(0)^2)=921$

$P = a+b+c = 1983.61$

$A = (.5)(921)(265)=122032.5$

$r = 2*A/P=123.041$

$Q = c/2,r = (460.5,123.041)$

$k=r/(r-x) = 123.041/(123.041-(-25))= 0.831$

Solving for points A and C

$A’ = A+(Q-A) * k$

$Xa=0+(460.5-0)*.831 = 382.676$ Is this a vector from the inscribed center back towards 0? $Ya=0+(123.041-0)*.831 = 102.247$

$Xc=460.5+(460.5-460.5)x.831 = 460.5$

$Yc=265+(123.041-265)x.831= 147.197$

Would the inverse of k be $k'= (r+x)/r$ so if I wanted r to grow by 200 k would be

$k = (123.041+200)/123.041 = 2.621$?

I would comment in that question, but I do not have the reputation to do so, sorry for asking a question related to a solved problem but I'm really just not understanding the solution.

Could someone please show me how to arrive at the correct solution.

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I think I found the answer and the problem exists in the original question.

$k = R/(R-X)$

This is not accurate. Using the numbers above for points on the x-axis where y is 0 and solving for k using $A'=A+(Q-A)*k$ would give the following:

$25=0+(123.041-0)*k$

$k = 25/123.041 = .203$ which is just $X/r$