Question 21
In right triangle $ABC$ the hypotenuse $AB=5$ and leg $AC=3.$ The bisector of angle $A$ meets the opposite side in $A_1.$ A second right triangle $PQR$ is then constructed with hypotenuse $PQ=A_1B$ and leg $PR=A_1C.$ If the bisector of angle $P$ meets the opposite side in $P_1,$ the length of $PP_1$ is: