A car tried to ram the White House security barriers close to the US Capitol building at 15th Street NW and Pennsylvania avenue.
Marking 'A' on the map shows where the incident is thought to have happened.
Police chased the vehicle for about one and a half miles to 2nd Street and Constitution Avenue, near the Capitol, where the shots were fired.
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The band announced at a free concert on Friday that they would take over the event's Pyramid stage on Saturday June 25.
The victims were collecting permits and escorts a day after their home town was liberated from the extremists.
Scotland Yard said the male youths will appear in custody at Westminster Magistrates' Court on Saturday.