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England and Germany have a fierce football rivalry which has played out at both the World Cup and Euros.
A 4-3 aggregate victory sealed Real's progress to a remarkable sixth Champions League final in 10 years and they will bid for a record-extending 15th title against Borussia Dortmund at Wembley on June 1.
Bayern, with only the Champions League title left to fight for, had scored twice in four minutes early in the second half through a Leroy Sane strike and Harry Kane penalty to turn the game around before Vinicius' spot kick.
City's Bernardo Silva and Mateo Kovacic both misfired in the shootout to put Madrid in the driving seat.
Xabi Alonso's team, who have now gone a league-record 29 matches without defeat this season to secure their first trophy since 1993, have a 16-point lead over Bayern with five matches remaining.
Paris St Germain's Kylian Mbappe scored twice to lead them into the Champions League quarterfinals.
Bayern CEO Jan-Christian Dreesen said there would a 'a new direction' next season with a new coach.
The attacking full-back and dead-ball specialist became an instant Germany football great when his spot-kick earned them a 1-0 victory over Diego Maradona's Argentina in the World Cup final in Rome in 1990.
Rummenigge, a former longtime Bayern CEO, was West Germany's captain under coach Beckenbauer in the 1986 World Cup where they lost to Argentina in the final.
The German striker also added he would try to play cricket in his garden.
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