With a sharp knife, remove the peel and white pith from grapefruits and discard. Cut the grapefruit segments from the surrounding membranes, letting them drop into a small bowl. Working over a large bowl, squeeze the remaining membranes to extract the juice. Set the segments and juice aside separately.
Position rack in upper third of oven; preheat broiler. Line a broiler pan or baking sheet
Toss chicken, dry mustard, garlic powder, cinnamon, coriander, ginger, pepper and salt in a large bowl until the chicken is well coated. Place on the prepared pan in a single layer.
Broil the chicken until cooked through, about 5 minutes.
Meanwhile, whisk peanut butter, soy sauce, sugar and hot sauce into the reserved grapefruit juice until smooth. Add the cooked chicken and lettuce; toss to combine. Serve the salad topped with radishes and the reserved grapefruit segments.