There are two perpendicular lines, one touches to the circle `x^(2) + y^(2) = r_(1)^(2)` and other touches to the circle `x^(2) + y^(2) = r_(2)^(2)` if the locus of the point of intersection of these tangents is `x^(2) + y^(2) = 9`, then the value of `r_(1)^(2) + r_(2)^(2)` is.

Answer

To solve the problem, we need to analyze the given information step by step.

### Step 1: Understand the circles and their tangents
We have two circles:
1. Circle 1: \( x^2 + y^2 = r_1^2 \)
2. Circle 2: \( x^2 + y^2 = r_2^2 \)

Both circles are centered at the origin (0, 0) and have radii \( r_1 \) and \( r_2 \) respectively.

### Step 2: Identify the tangents
We are given that there are two perpendicular tangents to these circles. Let's denote the point of intersection of these tangents as \( (h, k) \).

### Step 3: Relate the tangents to the radii
Since the tangents are perpendicular, we can say that:
- One tangent touches Circle 1 at a point where the radius is \( r_1 \) (let's say vertically).
- The other tangent touches Circle 2 at a point where the radius is \( r_2 \) (let's say horizontally).

From the geometry of the situation, we can observe that:
- The vertical tangent will intersect the y-axis at \( k = r_1 \).
- The horizontal tangent will intersect the x-axis at \( h = r_2 \).

### Step 4: Use the locus condition
We are given that the locus of the point of intersection of these tangents is described by the equation:
\[ x^2 + y^2 = 9 \]

This means that for any point \( (h, k) \) on the locus, we have:
\[ h^2 + k^2 = 9 \]

### Step 5: Substitute the values of h and k
From our earlier observations, we have:
- \( h = r_2 \)
- \( k = r_1 \)

Substituting these into the locus equation gives:
\[ r_2^2 + r_1^2 = 9 \]

### Step 6: Rearranging the equation
We can rearrange this equation to find the desired expression:
\[ r_1^2 + r_2^2 = 9 \]

### Conclusion
Thus, the value of \( r_1^2 + r_2^2 \) is:
\[ \boxed{9} \]