Question on circles inscribed in a rectangle In rectangle $ABCD$, $AB = 8$ and $BC = 20$. Let $P$ be a point on $AD$ such that angle $\measuredangle BPC = 90^\circ$. If $r_1, r_2, r_3$ are the radii of the incircles of triangles $APB, BPC$ and $CPD$, what is the value of $r_1 + r_2 + r_3$?

Given the inradius equation for a right triangle, as hinted by @Joey, just replace the variables:
$$
\begin{eqnarray}
r_1 &=& \frac{AB + AP - BP}{2} \\
r_2 &=& \frac{CD + DP - CP}{2} \\
    &=& \frac{AB + (BC - AP) - CP}{2} \\
r_3 &=& \frac{BP + CP - BC}{2} \\
\end{eqnarray}
$$
And then simplify:
$$
\begin{eqnarray}
R &=& r_1 + r_2 + r_3 \\
  &=& \frac{AB + AP - BP}{2} +
              \frac{AB + (BC - AP) - CP}{2} +
              \frac{BP + CP - BC}{2} \\
  &=& AB \\
\end{eqnarray}
$$
So the total radii of the incircles is 8.
