1. **Problem Statement:** Given a line segment NT with length 12 cm, and NT = 12MT, find the radius of the semicircle drawn above NT. 2. **Understanding the problem:** The points M, N, and T lie on a horizontal line with NT = 12 cm. The semicircle is drawn above the segment NT, and we need to find its radius. 3. **Given:** - NT = 12 cm - NT = 12MT 4. **Find:** Radius of the semicircle. 5. **Step 1: Express MT in terms of NT.** Since NT = 12MT, we have $$ MT = \frac{NT}{12} = \frac{12}{12} = 1 \text{ cm} $$ 6. **Step 2: Find MN.** Since M, N, and T are collinear and arranged as M - N - T, $$ MN = NT - MT = 12 - 1 = 11 \text{ cm} $$ 7. **Step 3: Understand the semicircle radius.** The semicircle is drawn on segment NT, so its radius is half of NT: $$ \text{Radius} = \frac{NT}{2} = \frac{12}{2} = 6 \text{ cm} $$ 8. **Final answer:** The radius of the semicircle is **6 cm**. This is because the semicircle is drawn on the segment NT, and the radius of a semicircle is half the length of its diameter (NT).