1. Cut 4 of the cucumbers into 1-inch pieces and place them in a food processor or blender. Add the garlic, broth, 6 cups of the yogurt, 1½ cups of the mint, and the lemon juice. Process until smooth. Transfer the mixture to a large bowl. (If using a blender, prepare the puree in batches.)

2. Whisk in the remaining 2 cups yogurt and ½ cup mint. Season with salt and pepper. Chill, covered, for 2 to 3 hours.

3. Cut the remaining cucumber into ¼-inch dice and toss with the radishes. Divide the soup among eight bowls. Top each with the cucumber-radish mixture and serve immediately.