you can see in the lower right side of the picture the Kadik+Ãƒâ€šÃ‚Â¦y - Chalcedon (Asian Istanbul right across the Sea of Marmara)
This is how it looks from the sea today:
The church of St. Euphemia the Martyr was built in the fifth century AD and is a circular building standing in Sultanahmet Square. The most unique feature of this building is its very interesting frescos. One of these portrays the torture and death of Euphemia from Kadikoy who is believed to have been killed because of her religious beliefs.Though the church dedicated to St. Euphemia collapsed in 1951, its frescoes are preserved under an awning. Its original structure came about when the magnificent domed hall which was accessible form the Antiochus Palace was turned into a church in the 5th century. Destroyed after the conquest in 1453, the church is famous for its frescoes depicting the life of St. Euphemia as well as its ruins showing early church architecture. The remaining pieces from the chest containing St. Euphemias holy relices are preserved in the Church of St. George Church in Fener.
The location of the Church of St. Euphemia that you are reffering to can be found in site: http://www.istanbulambassadorhotel.com/istanbulmap/onelocation.php?locationid=245&categoryid=8
As you can see from the map, this church is not at Chalcedon, but in the main city of Constantinouple (Istanbul).
You can find the story of St. Euphemia in this site: http://saintgeorge.org/news_and_events/church_calendar/saint_of_the_day/09sep/sep_16_st_euphemia_the_martyr.php
There is a church at Chalcedon http://www.istanbulguide.net/istguide/artetarch/eglises/euphem.htm
that is dedicated to Her.
It is in 1694, that the m+Ãƒâ€šÃ‚Â¬tropolite of Chalc+Ãƒâ€šÃ‚Â¬doine (Kadik+Ãƒâ€šÃ‚Â¦y) have the authorization to rebuild this sanctuary on the ruins of a Byzantine church. It was financed by Russia and was dedicated to holy Euph+Ãƒâ€šÃ‚Â¬mie, virgin-martyr. The remainders of the holy are at the orthodoxe patriarchate of Phanar (Fener), except the head that was carried by the crusaders to the convent of Lucelle in the principality of Basle, at the time of the conquest of the city in 1204.
You can find the information for the place where the 4th Ecumenical Council took place in site:http://meltingpot.fortunecity.com/alexandra/849/IstanbulTour.htm
The entrance of the church:
The Icon of the Council: