Coronal waves exist ubiquitously in the solar atmosphere. They are important not only in their own rich physics but also essential candidates of triggering magnetic eruptions in the remote. However, the later mechanism has never been directly confirmed. By revisiting the successive eruptions on 2012 March 7, fast-mode shocks are identified to account for the X5.4 flare-related EUV wave with a velocity of 550 km/s, and appeared faster than 2060$pm$270 km/s at the front of the corresponding coronal mass ejection in the slow-rising phase. They not only propagated much faster than the local Alfven speed of about 260 km/s, but also simultaneously accompanied by type II radio burst, i.e., a typical feature of shock wave. The observations show that the shock wave disturbs the coronal loops C1 connecting active regions (ARs) 11429 and 11430, which is neighboring a null point region. Following a 40-min-oscillation, an external magnetic reconnection (EMR) occurred in the null point region. About 10 min later, a large-scale magnetic flux rope (MFR) overlaid by the C1 became unstable and erupted quickly. It is thought that the fast-mode shock triggered EMR in the null point region and caused the subsequent eruptions. This scenario is observed directly for the first time, and provides new hint for understanding the physics of solar activities and eruptions.
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