The image you provided shows a geometrical diagram involving a circle, labeled points, and what seems to be part of a curve. Let's break down what is represented in the diagram:

1. Circle:

   • The circle is centered at the origin $O(0, 0)$ with a certain radius.
   • The circle intersects the X-axis at two points, $D\left(\frac{1}{2}, 0\right)$ and $C\left(\frac{3}{2}, 0\right)$.
   • It also intersects the Y-axis at points $A\left(\frac{1}{2}, \sqrt{2}\right)$ and $B\left(\frac{1}{2}, -\sqrt{2}\right)$.

2. Axes:

   • The diagram shows the standard coordinate plane with the X-axis and Y-axis marked as $XOX'$ and $YOY'$ respectively.

3. Curve:

   • There's a curve labeled "(i)" that intersects the circle at points like $A$, following a specific path.
   • This curve likely represents a parabola or another conic section.

4. Point Labels:

   • Point $A \left( \frac{1}{2}, \sqrt{2} \right)$ is located on the Y-axis.
   • Point $D \left( \frac{1}{2}, 0 \right)$ lies on the X-axis.
   • Points $C \left( \frac{3}{2}, 0 \right)$ and $B \left( \frac{1}{2}, -\sqrt{2} \right)$ are other significant points of intersection on the circle and curve.

From the diagram, it seems like there might be an equation for the circle and the curve that could be explored further. If you'd like to dive deeper into finding the equations of the circle and curve or solve any related problems, feel free to ask!

Would you like a more detailed analysis or a solution to a specific question related to this diagram?

Related Questions:

1. What is the equation of the circle shown in the diagram?
2. What is the equation of the curve labeled "(i)" intersecting the circle?
3. How do we calculate the radius of the circle from the given points?
4. What type of conic section is represented by curve (i)?
5. Can you find the area of the region bounded by the circle and the curve?

Tip: Understanding the relationship between the circle and curve can help in calculating areas and solving integrals related to these figures.