BURLINGTON, N.C. — Becton, Dickinson could be on the verge of acquiring the 93.5 percent of TriPath Imaging stock the company doesn’t already own.

BD (NYSE: BDX) said Monday night that it had made a $350 million offer for TriPath (Nasdaq: TPTH), the Burlington-based provider of detection, diagnosis, staging and treatment solutions for cancer.

The news sent TriPath skyrocketing more than $3 a share after Monday’s close to $8.70.

The stock closed Tuesday at $8.82. up $3.70 or 72 percent, on the day.

Oddly, TriPath’s stock had hit a 52-week low of $5.12, down 27 cents, during normal trading on Monday.

BD, which is based in New Jersey, offered $9.25 a share for the 93.5 percent of TriPath’s 38,450,000 shares it doesn’t already own. That price represented an 81 percent premium over Monday’s closing price.

TriPath executives solicited the offer, both companies said in statements.

“The proposal was solicited by TriPath Imaging in connection with the culmination by TriPath Imaging of a process to explore strategic alternatives,” BD said in its statement. A takeover of TriPath “fits strategically with BD’s objective of accelerating and advancing its presence in the cancer diagnostics market,” BD added.

Stephen Hall, a spokesman for TriPath, told MarketWatch that the company would evaluate the offer and declined further comment.

In a statement, TriPath said: “The proposal arose after a review by TriPath Imaging of potential strategic opportunities.”

TriPath and BD have worked together since 2001 to develop and commercialize diagnostic products for melanoma and cancer of the cervix, breast, ovary and prostate.

“Since TriPath Imaging and BD have not entered into a definitive agreement, further discussion of the proposal would be premature at this time,” TriPath added.

TriPath: www.tripathimaging.com