Why were Europeans interested in the ideas of Mathematician al-Khwarizmi and physicians Muhammad al-Razi and Ibn Sina

Because they revolutionized sciences of the time. They all discovered many new things in their respective fields that were way above the level of European scientists. For example, al-Khwarizmi discovered algebra and made textbooks on complex mathematics, while Al-Razi for example made new discoveries in the field of therapy and developed fields like ophthalmology and pediatrics. Their works were translated into Latin because of how advanced for the time they were.