How did the Turks come to topple the Byznatine empire?

Answer 1

The Byzantines had lost ground to the Islamic empire (which quickly split into individual nations) for years on it's eastern front, and from successive migrations in the west, such as Slavs and Bulgars. Losing Egypt (historically one of the richest areas in the Mediterranian) permanently crippled the empire.

However, the empire managed to wax and wane for years, expanding and consolidating when they had effective and brilliant emperors, and suffering successive crises. The death knell came in 1204, when the Fourth Crusade sacked Constantinople, throwing the Emperors out for 50 years and looting the city.

However, the Turks still couldn't take the city, because the city was easily resupplied via the sea as well as from the European side. They consolidated their position in 1357, when Gallipoli was devastated by an earthquake, and they swiftly moved in to take the city and establish a foothold in Europe. This allowed them to choke Constantinople from the Anatolian plain as well as from the European side of the city.

The final blow was when Mehmed II brought the whole package together: he beseiged the European side, used his fleet to block the southern entrance, and constructed forts north of the city to block access from the Black Sea.

Note: You're in luck - I've been studying the fall of Constantinople :)

Answer 2

by their powers