Length of angle bisector of right angle in right angled triangle

In triangle BCA, /_ C =90॰ BC=a CA=b.  Bisector of /_C meets BA at D. Find length of CD. (Hint: draw BF perpendicular on CD.)

1) Find area of the triangle BCA.

2) Find hypotenuse BA.

3)Find length of perpendicular CF on hypo. BA

4) Find BD and DA by angle bisector property / theorem.

5) Find area of triangle BCD.

6) Find BF = a sin 45॰

7) From area of triangle BCD find CD. using CD as base and BF as height.

(ab x sq root 2)/(a+b)