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strike someone or something on something
to hit someone or something on a particular place or part. The ball struck me on my elbow, causing a great deal of pain. I struck the bear on the paw, and that only made it madder.
strike something (up)on something
to hit or bang something on something else. She struck her head upon the side of the bed. Mary struck her elbow on the doorjamb.
strike onor strike upon
To discover something suddenly or unexpectedly: In the course of their research, the scientists struck on an entirely new approach. The detective struck upon a clue.