title: Math problem: Determine the corner radius of an inner border based on outer corner radius/thickness
body: <p>Here's a math/geometry problem for the math whizzes (not my strongest subject). This is for WPF, but should be general enough to solve regardless:</p>
  
  <p>I have two embedded Border elements, with the outer one having a certain corner radius, <code>R</code> and border thickness, <code>T</code>. Given these two values, what should the corner radius of the inner Border, <code>R'</code> be set to such that the two corner edges meet with no overlap or holes?</p>
  
  <p><a href="https://i.stack.imgur.com/ef2FW.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ef2FW.png" alt="alt text"></a>
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  <p>So far I've just been eyeballing it, but if someone can give me a proper formula that would be great. Respect points if you can!! ;)</p>