Mark the center of a 3/8" dowel, insert dowel into existing hole, drill new
hole. A forstner bit might work best, depending on the original material.
Make a drill guide jig on a drill press with a through hole 3/8" dia. and a
concentric 1/2" dia. hole drilled halfway through (like a deep counterbore) a
scrap piece of wood. Use the small hole and bit to locate the jig, then clamp it
to your workpiece. Then use the large hole to guide the 1/2" bit.
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