In the problems for this issue, we consider triangle ABC where C is a right angle, and denote by a, b, and c the lengths of the sides opposite angles A, B and C.  Let AE and CD be the bisectors of angles A and C.  See Figures 1 through 3.

PROBLEM I

Find CD if a = b = √2 (Figure 1).

PROBLEM II

Find CD in terms of a and b (Figure 2).  Note that a need not equal b.

PROBLEM III

Find AE in terms of b and c (Figure 3).  As an example, if a = 96, b = 28, c = 100, then AE = 35.

The problems for this issue were suggested by problem mm-1649 in the June 2002 issue of the Mathematics Magazine.  "Prove that if a right triangle has all of its sides of integral length then it has at most one angle bisector of integral length".  My editor, Bryan Taylor, has approved extra credit for solvers of mm-1649 and this problem is suggested only for the retired or others with time on their hands.  Note that in problems 1 through 3 it is not required that the sides or bisectors have integral lengths. 

Send your solutions to Herb.Bailey@rose-hulman.edu or to Herb Bailey, Math. Dept., Rose-Hulman, 5500 Wabash Ave., Terre Haute IN 47803.

Answers to the summer problems were 4 and 728163549.  Solvers of the summer problems are listed on the left, and as an added feature I have included late and lost solvers of the spring problems.  These are marked with an asterisk.  Note, this will not be a regular feature.

Solvers of the summer problems are listed below:

Alumni:  A. Kelsal, 1940; B. Barrick, 1941;  W. Soudritte, 1943; D. Heath, 1943; T. Blickwedel, 1946; C. Cook, 1949; A. Junker, 1950; W. Rinker, 1951; D. Camp, 1955; C. Cooper, 1956; D. Bailey, 1959; C. Sechrest, 1960; J. Tindall, 1961; B. Teegardin, 1964; *S. James, 1965; J. Lafuze, 1967; J. Burke, 1968; R. James, 1968; B. Kraus, 1969; A. Mahler, 1971; S. Sample, 1971; D. Dvorak, 1972; D. Artman, 1976; M. Bailey, 1976; *S. Warner, 1978; R. Joyner, 1980; J. Carr, 1980; M. Muri, 1982; B. Dudley, 1983; D. Dillon, 1984; V. Hasler, 1984; C. Hastings, 1986; M. Walden, 1986; G. Fleck, 1986; S. Johnson, 1988; B. Shew, 1989; C. Abdnour, 1989; *G. Heimann, 1990; B. Burger, 1991; N. Wesseler, 1991; D. Hector, 1992; B. Hollis, 1994; P. Neukam, 1994; M. Young, 1994; R. Mohr, 1996; C. Tracy, 1997; T. Patterson, 1997; M. Pilcher, 1998; D. Sing, 2000; J. Trimm, 2001; *D. Harrington, 2002; and J. Lewis, 2006.