Find the position of the point $(5, 12)$ with respect to the circle $x^{2} + y^{2} = 169$ .

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Solution

Given the equation of the circle is $x^{2} + y^{2} = 169$ .
Now, $5^{2} + 12^{2} = 25 + 144 = 169$ .
So the point $(5, 12)$ lies on the circle $x^{2} + y^{2} = 169$ .

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