Question: What is the seat of the county in the state where Hamilton Southeastern High School is located in which Arcadia can be found?

full_context: Document 1: Northside Health Careers High School: Northside Health Careers High School (HCHS) is a magnet school in San Antonio's Northside Independent School District for students that are interested in pursuing a career in the health professions. HCHS attracts students from school districts all across Bexar County and some from as far as Hondo, Texas.
Document 2: 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 3: Hamilton Southeastern High School: Hamilton Southeastern High School (HSE or HSHS) is a four-star, former Blue Ribbon public high school in Fishers, Indiana, United States. It is a part of the Hamilton Southeastern School District.
Document 4: 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 5: 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 6: 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 7: 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 8: 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 9: 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 10: Rich East High School: Rich East High School or REHS is a public four-year high school located in Park Forest, Illinois, a southern suburb of Chicago in the United States. Rich East's campus serves the cities of Park Forest, Matteson, Olympia Fields, Chicago Heights and Richton Park serving sections of school districts 162 and 163. Oscar W. Huth Middle School, Illinois Elementary School, Barack Obama School of Leadership and STEM and Michelle Obama School of Technology and the Arts serves as feeder schools. It is a part of Rich Township District 227, which also includes Rich South High School and Rich Central High School.
Document 11: Hamilton High School (Anza, California): Hamilton High School is a public high school in Anza, California, United States. It became a true 9-12 high school in the school year 2006-2007.
Document 12: 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 13: 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 14: The Bronx: Many public high schools are located in the borough including the elite Bronx High School of Science, Celia Cruz Bronx High School of Music, DeWitt Clinton High School, High School for Violin and Dance, Bronx Leadership Academy 2, Bronx International High School, the School for Excellence, the Morris Academy for Collaborative Study, Wings Academy for young adults, The Bronx School for Law, Government and Justice, Validus Preparatory Academy, The Eagle Academy For Young Men, Bronx Expeditionary Learning High School, Bronx Academy of Letters, Herbert H. Lehman High School and High School of American Studies. The Bronx is also home to three of New York City's most prestigious private, secular schools: Fieldston, Horace Mann, and Riverdale Country School.
Document 15: Arcadia, Indiana: Arcadia is a town in Jackson Township, Hamilton County, Indiana, United States. The population was 1,666 at the 2010 census.
ground_truth: Noblesville
sub_queries: What is the name of the state where Hamilton Southeastern High School is located? Answer: Indiana
Arcadia, Indiana >> located in the administrative territorial entity Answer: Hamilton County
Hamilton County >> capital Answer: Noblesville