To solve for the length of the external tangent between two circles, we can use the formula:

$L = \sqrt{d^2 - (r_1 + r_2)^2}$

where:

• $d$ is the distance between the centers of the two circles,
• $r_1$ and $r_2$ are the radii of the circles.

Given Values:

• $d = 26$ cm
• Radius of the larger circle, $r_1 = 15$ cm
• Radius of the smaller circle, $r_2 = 11$ cm

Step-by-Step Solution:

1. Sum of the Radii: $r_1 + r_2 = 15 + 11 = 26 \text{ cm}$

2. Substitute in the Formula: Since $d = 26$ cm and $r_1 + r_2 = 26$ cm: $L = \sqrt{26^2 - 26^2} = \sqrt{0} = 0$

Conclusion:

The length of the external tangent $L$ is $0$ cm, meaning that the circles are just touching externally, so no external tangent exists that would form a segment between them.

Would you like more details on why the external tangent length is zero in this case, or have any further questions?

Here are five related questions that may deepen understanding:

1. What happens to the external tangent if the circles are separated by a larger distance?
2. How would we calculate the internal tangent if needed?
3. How does the distance between centers affect tangent properties?
4. How would this change if one circle was inside the other?
5. Can we generalize this method to circles of any radius and separation?

Tip: For any two circles that touch externally, the external tangent length is zero because they intersect at exactly one point.