Halve cucumber lengthwise, then slice crosswise 2 centimeters / 1 inch thick.
Bring vinegar, water, sugar, and salt to a boil in a saucepan, then cool to room temperature.
Combine cucumber, radish, and vinegar in a bowl and chill, covered, until cold. Drain vegetables before serving.
Makes 4 servings.
Pickled vegetables may be chilled up to 3 hours.