The image you provided shows a right triangle inside a quarter circle. Let's analyze it step by step to solve for $x$.

1. Dimensions:

   • The quarter circle has radius 5 (from the total vertical height, 4 + 1).
   • The base from $O$ to $B$ is divided into two parts: $OB = 3 + 2 = 5$.
   • The pink line $x$ is the hypotenuse of the right triangle with legs 3 and 4.

2. Using Pythagoras Theorem: In a right triangle, the relation between the legs and the hypotenuse is given by: $x^2 = \text{leg}_1^2 + \text{leg}_2^2$ Here, the legs are 3 and 4.

$x^2 = 3^2 + 4^2$ $x^2 = 9 + 16 = 25$ $x = \sqrt{25} = 5$

Thus, $x = 5$.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. What is the length of the diagonal in a right triangle with legs 5 and 12?
2. How would you calculate the area of a quarter circle with radius 5?
3. If the radius of the quarter circle was doubled, how would the value of $x$ change?
4. What would the perimeter of the triangle in the image be?
5. How would you calculate the area of the triangle formed in the image?

Tip: Always apply the Pythagorean Theorem to right triangles to find missing sides when two sides are known.