A ball rolls into a corner of a room, where it touches both walls (and, obviously, the floor). A

larger ball rolls into the same corner so that it touches both walls and the first, smaller ball.
The small ball has a radius 1 inch. What is the radius of the large ball?

I don't want the answer, I just want to know how to find the answer.

To find the radius of the larger ball, we can use the concept of tangent circles. Tangent circles are circles that touch each other at exactly one point without overlapping. In this scenario, the larger ball and the smaller ball form tangent circles.

Here are the steps to find the radius of the larger ball:

1. Consider the smaller ball as Circle A and the larger ball as Circle B.
2. Draw a diagram to visualize the scenario. Draw two vertical lines representing the walls of the corner and a horizontal line representing the floor. Place the smaller circle touching both walls and the floor.
3. Note that the point of contact between the two balls lies on a line perpendicular to the floor because both balls are touching the floor.
4. Draw a line from the center of Circle A (smaller ball) to the point of contact between the two balls. Let's label this line segment as 'd'.
5. Draw a line from the center of Circle B (larger ball) to the point of contact between the two balls. Let's label this line segment as 'D'.
6. Since the two circles are tangent, the radii of both Circle A and Circle B are perpendicular to the line segment connecting the centers of the two circles.
7. By drawing a line segment perpendicular to the floor from the center of Circle A, label the length of this segment as 'h'.
8. By drawing a line segment perpendicular to the floor from the center of Circle B, label the length of this segment as 'H'.
9. Now you can see two right triangles formed, one with sides 'h', '1', and 'd', and the other with sides 'H', 'r', and 'D'.
10. The ratios of corresponding sides in similar triangles are equal. Set up the proportion:
h / 1 = H / r
11. Since we know the radius of Circle A is 1 inch, substitute the value of 'h' as 1 in the proportion.
1 / 1 = H / r
12. Simplify the equation to solve for the radius 'r' of Circle B:
H = r
13. The radius of the larger ball (Circle B) is the same as the length of line segment 'H'.

By following these steps, you can determine the radius of the larger ball.