To find the length of leg $x$, we can apply the Pythagorean theorem since the given information suggests a right triangle.

Given:

• The radius of the circle is 4 cm.
• One leg of the triangle is also 4 cm.
• The hypotenuse is the radius of the circle (4 cm).

We can label the sides of the right triangle as:

• One leg is 4 cm (given).
• The other leg is $x$ (the unknown we're solving for).
• The hypotenuse is the radius of the circle, which is also 4 cm.

Step 1: Apply the Pythagorean theorem:

$a^2 + b^2 = c^2$ Where:

• $a$ and $b$ are the legs of the right triangle,
• $c$ is the hypotenuse.

Substitute the known values: $4^2 + x^2 = 4^2$

Step 2: Solve for $x$:

$16 + x^2 = 16$ $x^2 = 16 - 16 = 0$ $x = \sqrt{0} = 0$

Conclusion:

The length of leg $x$ is 0 cm.

Would you like further clarification on the reasoning or any additional questions on this topic?

Additional questions:

1. How would the result change if the hypotenuse was longer than the radius?
2. What if one of the legs was shorter than the radius but longer than the other leg?
3. How would we apply the Pythagorean theorem to an obtuse triangle?
4. Can this method be used for non-right triangles? If so, how?
5. How can we use trigonometric ratios to find the sides of a right triangle?

Tip: The Pythagorean theorem is only valid for right-angled triangles, so make sure the triangle you're working with is indeed a right triangle!