P, Q, R are the centres and `r_(1),r_(2),r_(3)` are the radii respectively of three coaxial circles, then
`QR r_(1)^(2)+RP r_(2)^(2) +PQ r_(3)^(2)=PQ.QR.RP`

Answer

To solve the problem, we need to verify the equation involving the distances between the centers of three coaxial circles and their respective radii. The equation we need to check is:

\[ QR \cdot r_1^2 + RP \cdot r_2^2 + PQ \cdot r_3^2 = PQ \cdot QR \cdot RP \]

### Step-by-Step Solution:

1. **Identify the Centers and Radii**:
Let \( P, Q, R \) be the centers of the three coaxial circles, and let \( r_1, r_2, r_3 \) be the radii of these circles respectively.

2. **Determine the Distances**:
- The distance \( QR \) can be expressed as \( QR = |Q - R| \).
- The distance \( RP \) can be expressed as \( RP = |R - P| \).
- The distance \( PQ \) can be expressed as \( PQ = |P - Q| \).

3. **Calculate the Squares of the Radii**:
- The radius \( r_1 \) of the circle centered at \( P \) can be calculated using the formula:
\[ r_1^2 = g_1^2 + f_1^2 - c_1 \]
- Similarly, calculate \( r_2^2 \) and \( r_3^2 \) for circles centered at \( Q \) and \( R \) respectively.

4. **Substitute Values into the Left-Hand Side (LHS)**:
Substitute the distances and the squares of the radii into the left-hand side of the equation:
\[ LHS = QR \cdot r_1^2 + RP \cdot r_2^2 + PQ \cdot r_3^2 \]

5. **Substitute Values into the Right-Hand Side (RHS)**:
Calculate the right-hand side:
\[ RHS = PQ \cdot QR \cdot RP \]

6. **Compare LHS and RHS**:
After substituting the values into both sides, simplify both sides to see if they are equal.

7. **Conclusion**:
If the left-hand side does not equal the right-hand side, the statement is false.