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Let \( f \) be a non-negative function defined on the
\( \mathrm{P}^{190} \) interval \( [0,1] \). If \( \int_{0}^{x} \sqrt{1-\left(f^{\prime}(t)\right)^{2}} d t=\int_{0}^{x} f(t) d t \),

W \( 0 \leq x \leq 1 \) and \( f(0)=0 \), then
(1) \( f\left(\frac{1}{2}\right)\frac{1}{2} \) and \( f\left(\frac{1}{3}\right)\frac{1}{3} \)
(2) \( f\left(\frac{1}{2}\right)\frac{1}{2} \) and \( f\left(\frac{1}{3}\right)\frac{1}{3} \)
(3) \( f\left(\frac{1}{2}\right)\frac{1}{2} \) and \( f\left(\frac{1}{3}\right)\frac{1}{3} \)
(4) \( f\left(\frac{1}{2}\right)\frac{1}{2} \) and \( f\left(\frac{1}{3}\right)\frac{1}{3} \)
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