Two Circles and One Tangent

How to Find the Distance between the Circles's Centers

Example 1

$$ HZ $$ is a tangent connecting to the 2 circles. What is the distance between the centers of the circles?

Example 2

$$ HZ $$ is a tangent connecting to the 2 circles. What is the distance between the centers of the circles?

Problem 1

KL is tangent to both circle W and Circle P.
What is the distance between the centers of the circles below?

Distance between two circles connected by a tangent
Step 1
Create the rectangle.
Step 2
$ WP^2 = 6^2 + 24^2 \\ WP = \sqrt{ 6^2 + 24^2 } \\ \text{m } \overline{WP} \approx 24.7 $
Problem 2

What is the distance between the centers of the circles connected by tangent KL?

Tangent of Two Circles
$ WP^2 = 40^2 + 30^2 \\ WP = \sqrt{ 40^2 + 30^2 } \\ \text{m } \overline{ WP } = 50 $
Problem 3

What is the distance between the centers of the circles connected by tangent KL?

Tangent of Two Circles
$ WP^2 = 80^2 + 60^2 \\ WP = \sqrt{ 80^2 + 60^2 } \\ \text{m } \overline{ WP } = 100 $
Problem 4

What is the distance between the centers of the circles O and R, connected by tangent HZ?

Tangent of Two Circles
tangent to circle
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