Sum of the squares of the length of the tangents from the points (18, 18), (10, 20) and (21, 21) to the circle `x^(2) + y^(2) =25` is equal to ________ .

Explanation

To find the sum of the squares of the lengths of the tangents from the points (18, 18), (10, 20), and (21, 21) to the circle given by the equation \(x^2 + y^2 = 25\), we can use the formula for the length of the tangent from a point \((a, b)\) to a circle centered at the origin with radius \(r\):

\[ L = \sqrt{a^2 + b^2 - r^2} \]

In this case, the radius \(r\) of the circle is \(5\) (since \(r^2 = 25\)). Therefore, we will calculate the length of the tangents for each point and then find the sum of their squares.

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