1. **State the problem:** Find the length of the radius of the circle given the chords and radii in the diagram. 2. **Given:** - Vertical chord length = 6 - Horizontal chord length = 4 - Two radii forming part of the triangle = 6 each 3. **Understanding the problem:** The radius is the distance from the center of the circle to any point on the circle. 4. **Use the Pythagorean theorem:** The right triangle formed has legs 4 and 6, and the hypotenuse is the radius $r$. 5. **Apply the formula:** $$r = \sqrt{4^2 + 6^2}$$ 6. **Calculate:** $$r = \sqrt{16 + 36} = \sqrt{52}$$ 7. **Simplify:** $$r = \sqrt{4 \times 13} = 2\sqrt{13}$$ 8. **Approximate:** $$r \approx 2 \times 3.6055 = 7.211$$ 9. **Final answer:** The radius length is approximately **7.2 cm** to the nearest tenth.