Let's break the problem down and use geometry to find the radius of the circle.

Given:

• A straight line bisects the circle, but does not pass through the center.
• The length of the bisection is 20 cm.
• The distance from the midpoint of the bisection to the edge of the circle is 1 cm.

Let’s visualize this with the following notation:

• $O$ = the center of the circle.
• $r$ = the radius of the circle.
• The bisection line intersects the circle at two points, and it is 20 cm long.
• The midpoint of the bisection is 1 cm away from the edge of the circle.

Key Geometry:

The line bisects the circle but does not pass through the center. This means it is a chord that is not a diameter. The length of the chord is given as 20 cm, and the perpendicular distance from the center of the circle to the chord (let’s call this distance $d$) is $r - 1$ cm, because the distance from the midpoint to the edge is given as 1 cm.

Step 1: Use the chord length formula

For a chord of length $L$ and distance $d$ from the center, the relationship between the radius $r$, the length of the chord $L$, and the distance $d$ from the center is given by the formula:

$L^2 = 2r^2 - 2d^2$

Where:

• $L = 20$ cm (length of the chord),
• $d = r - 1$ cm (perpendicular distance from the center to the chord),
• $r$ is the radius of the circle.

Step 2: Plug in the values

Substitute the known values into the formula:

$20^2 = 2r^2 - 2(r - 1)^2$

$400 = 2r^2 - 2(r^2 - 2r + 1)$

$400 = 2r^2 - 2r^2 + 4r - 2$

Simplify:

$400 = 4r - 2$

Step 3: Solve for $r$

Now, solve for $r$:

$400 + 2 = 4r$

$402 = 4r$

$r = \frac{402}{4} = 100.5 \text{ cm}$

Conclusion:

The radius of the circle is 100.5 cm.

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Would you like more details on how the formula was derived or have any questions about this solution?

Here are 5 related questions you could explore:

1. How can we derive the formula for the relationship between a chord length and its perpendicular distance from the center?
2. How does the radius of the circle change if the bisection is further from the center?
3. What would happen if the line passed through the center of the circle instead of bisecting it?
4. How would you calculate the area of the circle once the radius is known?
5. What are some applications of this type of geometry in real-world problems?

Tip: When dealing with geometry problems like this, drawing a diagram and labeling key points like the center, chord, and distances can help clarify the relationships between the elements.