Corner Portfolio - when do we combine it with risk free rate

I have been trying to get an answer by reading all the past posts on corner portfolios and when to combine with the risk-free asset or with another portfolio, however, it doesn’t seem I found the answer I needed.

In one of the curriculum examples, they found the strategic asset allocation by combining this corner portfolio with the risk-free rate while I solved the problem by combining 2 corner portfolios. What confuses me is why did they combine the corner portfolio with the risk-free rate? The problem said asset class weights to be non-negative. So now I am unsure to when I should be combining the portfolio with another portfolio and when to combine it with the risk-free rate