  We compute the decay widths for the neutral and singly-charged Higgs bosons
in the Georgi-Machacek model into the final states $\gamma\gamma$, $Z\gamma$,
and $W\gamma$. These decays are most phenomenologically interesting for the
fermiophobic custodial fiveplet states $H_5^0$ and $H_5^{\pm}$ when their
masses are below threshold for decays into $WW$, $ZZ$, or $WZ$. We study the
allowed branching ratios into these final states using scans over the allowed
parameter space, and show how the model can be constrained by LEP searches for
a fermiophobic Higgs boson decaying to two photons. The calculation involves
evaluating one-loop diagrams in which the loop contains particles with two
different masses, some of which do not appear in the existing literature. We
give results for these diagrams in a form convenient for numerical
implementation using the LoopTools package.
