Problem: In right triangle ABC the hypotenuse AB=5 and leg AC=3. The bisector of angle A meets the opposite side in A1​. A second right triangle PQR is then constructed with hypotenuse PQ=A1​B and leg PR=A1​C. If the bisector of angle P meets the opposite side in P1​, the length of PP1​ is:
Answer Choices:
A. 436​​
B. 435​​
C. 433​​
D. 232​​
E. 16152​​
Solution:
Let BA1​=x∴4−xx​=35​,x=25​ and 4−x=23​.∴PR=4−x=23​ and PQ=x=25​.
∴△PQR∼△BAC, the ratio of the sides being 1:2. In △BAC,AA1​2=32+(23​)2=445​∴AA1​=235​​ But PP1​:AA1​=1:2∴PP1​=21​⋅235​​=435​​.