1. **State the problem:** We have a semicircle with a diameter of 212 cm and a height (radius) of 35 cm. We want to understand the relationship between these values and verify the semicircle's properties. 2. **Formula and rules:** The diameter $d$ of a circle is twice the radius $r$, so $d = 2r$. 3. **Calculate the radius:** Given the diameter $d = 212$ cm, the radius is $$r = \frac{d}{2} = \frac{212}{2} = 106 \text{ cm}.$$ 4. **Check the height:** The height of the semicircle from the baseline to the top is the radius, which should be 106 cm, but the problem states the height is 35 cm. 5. **Interpretation:** The height 35 cm is less than the radius 106 cm, so the dashed line at height 35 cm is a chord parallel to the diameter, not the radius. 6. **Equation of the semicircle:** Centered at the origin, the semicircle's equation is $$y = \sqrt{r^2 - x^2} = \sqrt{106^2 - x^2} = \sqrt{11236 - x^2}.$$ 7. **Height line:** The horizontal line at height 35 cm is $$y = 35.$$ 8. **Find the chord length at height 35:** Solve for $x$ when $y=35$: $$35 = \sqrt{11236 - x^2} \implies 35^2 = 11236 - x^2 \implies x^2 = 11236 - 1225 = 10011.$$ 9. **Calculate $x$:** $$x = \sqrt{10011} \approx 100.05 \text{ cm}.$$ 10. **Chord length:** The chord length at height 35 cm is twice $x$: $$2x \approx 2 \times 100.05 = 200.1 \text{ cm}.$$ **Final answer:** The semicircle has radius 106 cm, diameter 212 cm, and the chord at height 35 cm has length approximately 200.1 cm.