Question: What is the capital of the county where Arcadia is located in the state where Lafayette is also found?

full_context: Document 1: Lake Lafayette: Lake Lafayette is a prairie lake located in the coastal lowland in eastern Tallahassee, Leon County, Florida with US 27 / State Road 20 running close on its south side.
Document 2: Arcadia Township, Carroll County, Iowa: Arcadia Township is one of eighteen townships in Carroll County, Iowa, USA. As of the 2000 census, its population was 752.
Document 3: Harrison Township, Wayne County, Indiana: Harrison Township is one of fifteen townships in Wayne County, Indiana, United States. As of the 2010 census, its population was 392 and it contained 138 housing units.
Document 4: Cedar Rapids, Iowa: As of the 2010 United States Census, the city population was 126,326. The estimated population of the three - county Metropolitan Statistical Area, which includes the nearby cities of Marion and Hiawatha, was 255,452 in 2008. Cedar Rapids is an economic hub of the state, located in the core of the Interstate 380.
Document 5: Center Township, Wayne County, Indiana: Center Township is one of fifteen townships in Wayne County, Indiana, United States. As of the 2010 census, its population was 7,579 and it contained 3,204 housing units.
Document 6: Wayne Township, Allen County, Indiana: Wayne Township is one of twenty townships in Allen County, Indiana, United States. As of the 2010 census, its population was 103,803.
Document 7: Lafayette, Madison County, Ohio: Lafayette is a census-designated place in the center of Deer Creek Township, Madison County, Ohio, United States. It is located at , along U.S. Route 40, just west of its intersection with U.S. Route 42.
Document 8: Arcadia, Indiana: Arcadia is a town in Jackson Township, Hamilton County, Indiana, United States. The population was 1,666 at the 2010 census.
Document 9: Arcadia, North Carolina: Arcadia is an unincorporated community in Davidson County, North Carolina. It is located in the northwestern section of the county along NC Highway 150. Neighboring communities and municipalities include Midway, Welcome, and Winston-Salem.
Document 10: Jackson Township, Clinton County, Indiana: Jackson Township is one of fourteen townships in Clinton County, Indiana. As of the 2010 census, its population was 1,173 and it contained 469 housing units. The township was named for President Andrew Jackson.
Document 11: Lafayette metropolitan area, Indiana: The Lafayette, Indiana Metropolitan Statistical Area, as defined by the United States Census Bureau, is an area consisting of three counties in Indiana, anchored by the city of Lafayette. As of the 2010 census, the MSA had a population of 235,013.
Document 12: Wayne Township, Hamilton County, Indiana: Wayne Township is one of nine townships in Hamilton County, Indiana, United States and serves as one of two townships within Noblesville, Indiana's jurisdiction. As of the 2010 census, its population was 7,886 and it contained 3,252 housing units, an increase from 2415 in 2000, as Noblesville continues to expand eastward and Fishers reaches its northern limits. In 2007, Noblesville officially opened one of the largest mixed use developments in the state, called the Noblesville Corporate Campus. A portion of the development is located within the township. When completed, it will include a large industrial/commercial park, several housing developments, hotels, greenspace and a large outdoor shopping center called Hamilton Town Center, being built by the Simon Property Group, headquartered in nearby Indianapolis.
Document 13: Center Township, Marion County, Indiana: Center Township is one of nine townships in Marion County, Indiana, in the United States. As of the 2010 census, its population was 142,787 and it contained 76,872 housing units. It is the most populated township in Marion County.
Document 14: Arcadia, Oklahoma: Arcadia is a town in Oklahoma County, Oklahoma, United States, and a part of the Oklahoma City metropolitan area. The population was 247 at the 2010 census, a decrease of 11.5 percent from 279 at the 2000 census.
Document 15: Des Moines metropolitan area: The Des Moines metropolitan area, officially known as the Des Moines -- West Des Moines, IA Metropolitan Statistical Area (MSA), consists of five counties in central Iowa, United States: Polk, Dallas, Warren, Madison, and Guthrie. The 2010 census population of these counties was 569,633, and the 2017 estimated population was 645,911.
ground_truth: Noblesville
sub_queries: Lafayette >> located in the administrative territorial entity Answer: Indiana
Arcadia, Indiana >> located in the administrative territorial entity Answer: Hamilton County
Hamilton County >> capital Answer: Noblesville