I have a homework problem asking me to find the constant c that will make the statistic have a t-distribution. The rv X1...X5 are iid with a standard normal distribution.

The statistic is:

T = c(X1 + X2)/sqrt (X3^2+X4^2+X5^2)

I see that the denominator looks like a Chi-Square with 3df and the numerator could be the summation of X. I know I need X-N(0,1) in numerator and U-Chi(rdf) in denominator for a t-distribution t(rdf). I want to square both sides to start but that looks more like a F-distribution. Any hints would be appreciated.

Thanks

Fred1956