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'striking distance' is correct and can be used in written English.
This idiom is used to refer to the point or state at which something is close to being achieved or accomplished. For example, "The voting results are within striking distance, so we may be able to turn the tables yet."
Dictionary
striking distance
noun
A distance at which a soldier, military force, vessel, etc. is sufficiently near to be able to attack an opponent.
Exact(60)
"I'm definitely within striking distance".
"We're within striking distance," Wright said.
Now I was within striking distance.
Striking distance is one thing; up and running is another.
They are within striking distance of taking several other houses.
Meanwhile, Trevino, Irwin and Quigley moved within striking distance.
But we're within striking distance of taking that city.
Italy's Giovanni Soldini was also within striking distance.
For one thing, it is within striking distance of Hackney.
After six years, they are now within striking distance.
He kept them within striking distance before finally taking over.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com