Question: What is the capital of the county that contains the city of Arcadia, in the state where Greenfield-Central High School is located?

full_context: Document 1: 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 2: Greenfield-Central High School: Greenfield-Central High School is a secondary school (grades 9-12) located in the city of Greenfield, Indiana. Under the management of the Greenfield-Central Community School Corporation. It had 1,363 students in 2009–2010.
Document 3: Central High School (Martinsburg, Pennsylvania): Central High School in Martinsburg, Pennsylvania is the smallest of the three Central High Schools in the commonwealth of Pennsylvania with 674 students in four grades (9-12). Central High opened in 1960 with the merging of Roaring Spring High School, Morrison Cove High School, and Martinsburg High School; becoming the first and only high school in Spring Cove School District history.
Document 4: Manchester Central High School: Manchester High School Central is the oldest public high school in the state of New Hampshire. Located in the heart of Manchester, New Hampshire, approximately 2,100 students attend from communities such as Candia, Hooksett, and Manchester. The name was changed from Manchester High School in 1922 when Manchester West High School opened. Including Central, Manchester has a total of three public high schools.
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: 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 7: 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 8: 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 9: 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 10: 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 11: 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 12: Grove City High School: Grove City High School is a high school in Grove City, Ohio, United States. It is one of the five high schools in the South-Western City Schools district. It houses about 1,900 students in grades 9-12. Formerly Jackson High School, Grove City High School moved from the former Park Street building in 1970, where it had been located since 1929. Grove City High School was chartered in the fall of 1895. The average classroom experience of GCHS teachers is 15.89 years. 46 teachers have bachelor's degrees and 63 have master's degrees or beyond. Special training has included TESA, Continuous Quality Improvement (CQI) training, site-based leadership training, integrated learning, alternative assessment, and alternative classroom management. Grove City High School has been A School Of Excellence for five years now.
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, Indiana: Arcadia is a town in Jackson Township, Hamilton County, Indiana, United States. The population was 1,666 at the 2010 census.
Document 15: Greenwich Village High School: Greenwich Village High School (GVHS) is a planned grade 9-12 independent high school in Manhattan, New York City. The school is located at 30 Vandam Street between 6th Avenue and Varick. GVHS was scheduled to open in September 2009.
ground_truth: Noblesville
sub_queries: What is the name of the state where Greenfield-Central High School is located? Answer: Indiana
Arcadia, Indiana >> located in the administrative territorial entity Answer: Hamilton County
Hamilton County >> capital Answer: Noblesville