
Step 1: Exploring potential utility objects.
- Old tyres can be creatively repurposed into functional objects, such as:
- Furniture (chairs, tables, swings).
- Playground equipment (climbing structures, jungle gyms).
- Decorative or practical planters.
- Artistic installations using recycled tyres.
Step 2: Conceptualizing the design. - Select an object that maximizes the use of tyre shapes.
- Utilize different tyre sizes and arrangements for structural stability.
- Maintain a balance between functionality and aesthetics.
Step 3: Illustrating the design.
- Provide a clear front-view sketch of the object.
- Include annotations to describe the integration of tyres.
- Apply texture and shading to enhance realism.



Let $ P(x_1, y_1) $ and $ Q(x_2, y_2) $ be two distinct points on the ellipse $$ \frac{x^2}{9} + \frac{y^2}{4} = 1 $$ such that $ y_1 > 0 $, and $ y_2 > 0 $. Let $ C $ denote the circle $ x^2 + y^2 = 9 $, and $ M $ be the point $ (3, 0) $. Suppose the line $ x = x_1 $ intersects $ C $ at $ R $, and the line $ x = x_2 $ intersects $ C $ at $ S $, such that the $ y $-coordinates of $ R $ and $ S $ are positive. Let $ \angle ROM = \frac{\pi}{6} $ and $ \angle SOM = \frac{\pi}{3} $, where $ O $ denotes the origin $ (0, 0) $. Let $ |XY| $ denote the length of the line segment $ XY $. Then which of the following statements is (are) TRUE?