PRECIOUS-Gold steadies below 3-week high, silver hits 5-1/2-month high

* Dollar index pares losses from near 8-month low

* Silver rallies to highest since late October

* Silver at its most expensive vs gold in 3 months

* GRAPHIC-Gold/silver ratio: (Recasts; updates prices; adds comment, byline, NEW YORK dateline)

By Marcy Nicholson and Jan Harvey

NEW YORK/LONDON, April 12 (Reuters) - Gold was flat after rising to three-week highs on Tuesday as the dollar nudged up from a near 8-month low against a basket of currencies, with the rally in oil helping to improve risk appetite, while silver rose to a 5-1/2-month high.

Spot gold touched a high of $1,262.60 an ounce before easing back to $1,257.01 by 3:49 p.m. EDT (1949 GMT), little changed from late on Monday. U.S. gold futures for June delivery settled up 0.2 percent at $1,260.90 an ounce.

Silver rose for the fourth straight session, gaining as much as 2 percent to $16.21 an ounce, the highest for the spot market since Oct. 28.

“The market may be thinking that inflation’s going up so metals are going up,” said Dan Pavilonis, senior market strategist for RJO Futures in Chicago.

“Then you see markets like silver and copper technically looking like they’re going to break out. That entices traders to come in and start buying it.”

Brent crude oil prices hit a four-month high and energy equities rose.

The bullion prices are being driven by the poor performance of the dollar and of stock markets, Afshin Nabavi, head of trading at MKS in Switzerland, said, with silver driving the market.

“If silver continues, gold should break above $1,265 and eventually move towards $1,300,” he said.

The gold/silver ratio, which measures the number of silver ounces needed to buy an ounce of gold, hit its lowest in two months as silver outperformed gold. An ounce of gold now buys 77.7 ounces of silver, compared with 83.3 ounces in late February.

Speculation that interest rates will stay low also helped gold and silver in their own right. Rising rates lift the opportunity cost of holding non-yielding assets such as bullion.

“Negative yields in my opinion remain the key reason for buying gold, and silver. That story will not go away,” Saxo Bank’s head of commodities research Ole Hansen said.

“(Gold) found the expected resistance at $1,255 and it was only when silver took off that it managed to get through. Silver ETF holdings have risen strongly this past month while gold has been almost flat. That could indicate some switch in focus to silver, and the move yesterday highlighted that.”

Among other precious metals, platinum was up 1.2 percent at $1,000.25 an ounce the highest since March 8, and palladium was up 0.2 percent at $546.26 an ounce.