Homophily, the tendency of people to associate with others similar to themselves, is observed in many social networks, ranging from friendships to marriages to business relationships, and is based on a variety of characteristics, including race, age, gender, religion, and education. We present a technique for distinguishing two primary sources of homophily: biases in the preferences of individuals over the types of their friends and biases in the chances that people meet individuals of other types. We use this technique to analyze racial patterns in friendship networks in a set of American high schools from the Add Health dataset. Biases in preferences and biases in meeting rates are both highly significant in these data, and both types of biases differ significantly across races. Asians and Blacks are biased toward interacting with their own race at rates >7 times higher than Whites, whereas Hispanics exhibit an intermediate bias in meeting opportunities. Asians exhibit the least preference bias, valuing friendships with other types 90% as much as friendships with Asians, whereas Blacks and Hispanics value friendships with other types 55% and 65% as much as same-type friendships, respectively, and Whites fall in between, valuing other-type friendships 75% as much as friendships with Whites. Meetings are significantly more biased in large schools (>1,000 students) than in small schools (<1,000 students), and biases in preferences exhibit some significant variation with the median household income levels in the counties surrounding the schools.