From your description of the map the torch projected onto the wall, Geirfast thinks the secret chamber must lie somewhere within Nud-melek, perhaps in the southern part of the Second Hall.
'The entrance to the chamber lies somewhere in the Second Hall, I think.'1/1
1 Enter areaDiscover the entrance to the secret chamber1/1
2 Speak toGeirfast (Show dialog)
'Amazing, you found it! Now that we know where it is, getting there again will be much quicker.
'You may wish to bring a friend or two if you are going to plumb the secrets of this chamber. Who knows what dangers may lie within?
'I suspect the strange riddles on the back of this map will help you in this last exploration. I will make you a fair copy of them, so you can bring them into the chamber with you.'1/1
'Can it be? You are the one? The axe you describe is known to me, but only in legend. It was prophesied that one not of our number -- the nearly forgotten secret council of Elves and dwarves -- would find it once more, within our ancient headquarters in the deepest recesses of the dwarf-mine.
'That map you found was a last desperate attempt to leave a record, should Dragonslayer's hiding place be forgotten -- a situation thought impossible then, but we did not forsee the rise of Durin's Bane, the abandonment of Khazad-dûm, and its degeneration into feared Moria. When Smaug was terrorizing the Lonely Mountain, some of us were instructed to search for records of where Dragonslayer might be hid and found nothing.
'You, brave ${RACE}, have discovered a treasure beyond compare. Lord Elrond shall be alerted, as well as Lady Galadriel... your name will be sung by council-members for Ages to come.'1/1