In a small bowl combine the olive oil, lemon, vinegar, garlic, salt, pepper, and mint; whisk together and set aside.
Slice the tomatoes and place them in the vinaigrette. Peel and slice the cucumbers and place them also in the vinaigrette. Gently toss the tomatoes and cucumbers to insure they are evenly coated. Leave the bowl to rest at room temperature for about 15 minutes.Arrange the tomatoes and cucumbers on chilled plates. Crumble the feta cheese onto the salads. Drizzle any remaining vinaigrette onto the salads. Serve with grilled pita or other flatbread.