Let \( L \) and \( M \) be the respective intersections of the internal and external angle bisec...

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Let \( L \) and \( M \) be the respective intersections of the internal and external angle bisectors of the triangle \( A B C \) at \( C \) and the side \( A B \) produced. If \( C L=C M \), then the value of \( \left(a^{2}+\right. \) \( b^{2} \) ) is (where \( a \) and \( b \) have their usual meanings)
(a) \( 2 R^{2} \)
(b) \( 2 \sqrt{2} R^{2} \)
(c) \( 4 R^{2} \)
(d) \( 4 \sqrt{2} R^{2} \)
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