I am married but attracted to a friend of mine at work. I do not have sexual feelings for her but care for her very much. Can this be a dangerous relationship to continue?
Of course it can be dangerous. Men desire to be the knight in shining armor to rescue the damsel in distress. What starts as no intentions of sexual feelings can decay, feeling as if you were blindsided, even though it was clearly building over time. Treat all relationships with the opposite sex with care and with the idea that it could become a problem if you are not on your guard.
Paul advised Timothy: "Do not rebuke an older man, but exhort him as a father, younger men as brothers, older women as mothers, younger as sisters, with all purity" (I Timothy 5:1-2). Notice the very last phrase. As Timothy dealt with various people, he was to keep in mind that the relationships had to be done with a pure mind and pure motives.
"Be sober, be vigilant; because your adversary the devil walks about like a roaring lion, seeking whom he may devour. Resist him, steadfast in the faith, knowing that the same sufferings are experienced by your brotherhood in the world" (I Peter 5:8-9).