Question: What is the capital of the county where Arcadia is located, in the state that contains Our Lady of Providence Junior-Senior High School?

full_context: Document 1: 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 2: Clark High School (Plano, Texas): R. C. Clark High School is a free co-educational secondary school in Plano, Texas (USA) serving grades nine and ten. Founded in 1978, the school is part of the Plano Independent School District. Hendrick Middle School, Carpenter Middle School, and Schimelpfenig Middle School feed into Clark. Students leaving Clark go on to attend Plano Senior High School. The school colors are red, white, and black, and the school mascot is the Cougar.
Document 3: 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 4: Charleston, South Carolina: The Roman Catholic Diocese of Charleston Office of Education also operates out of the city and oversees several K-8 parochial schools, such as Blessed Sacrament School, Christ Our King School, Charleston Catholic School, Nativity School, and Divine Redeemer School, all of which are "feeder" schools into Bishop England High School, a diocesan high school within the city. Bishop England, Porter-Gaud School, and Ashley Hall are the city's oldest and most prominent private schools, and are a significant part of Charleston history, dating back some 150 years.
Document 5: Latin School of Indianapolis: The Latin School of Indianapolis served from 1955 to 1978 as a pre-seminary boys' high school for the Roman Catholic Archdiocese of Indianapolis.
Document 6: 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 7: Our Lady of Providence Junior-Senior High School: Our Lady of Providence High School is a coed Catholic high school in Clarksville, Indiana, in the Roman Catholic Archdiocese of Indianapolis. The school first opened on September 12, 1951.
Document 8: 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 9: 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 10: Arcadia, Indiana: Arcadia is a town in Jackson Township, Hamilton County, Indiana, United States. The population was 1,666 at the 2010 census.
Document 11: 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 12: 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 13: Cathedral High School (Indianapolis): The school was founded as a boys high school by the Brothers of Holy Cross in 1918. In the 1970s, with the departure of the Brothers, a non-profit trust was developed by Robert V. Welch, other parents, and a lay board in an effort to keep Cathedral alive. As part of that change, the school moved from its longtime home in downtown Indianapolis to its present location at 56th and Emerson streets, the site of the former all-girls Ladywood St. Agnes Academy. This change also facilitated the admission of girls to Cathedral High School. The original location of the school at 1400 North Meridian Street is today the headquarters for the Roman Catholic Archdiocese of Indianapolis. On September 13, 2011, Cathedral celebrated its 93rd birthday and was formally re-affiliated with the Brothers of Holy Cross.
Document 14: 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 15: 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.
ground_truth: Noblesville
sub_queries: What state is Our Lady of Providence Junior-Senior High School located? Answer: Indiana
Arcadia, Indiana >> located in the administrative territorial entity Answer: Hamilton County
Hamilton County >> capital Answer: Noblesville