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The triangle formed by joining the three excentres \( \mathbf{I}_{1} \mathbf{I}_{2} \) and \( \mathbf{I}_{3} \) of \( \triangle A B C \) is called the excentral or excentric triangle and in this case internal angle bisector of triangle \( A B C \) are the altitudes of triangles \( \mathrm{I}_{1} \mathrm{I}_{2} \mathrm{I}_{3} \)
\( \mathrm{P} \)
Value of \( \mathrm{II}_{1}^{2}+\mathrm{I}_{2} \mathrm{I}_{3}^{2}=\mathrm{II}_{2}^{2}+\mathrm{I}_{3} \mathrm{I}_{1}^{2}=\mathrm{II}_{3}^{2}+\mathrm{I}_{1} \mathrm{I}_{2}^{2}= \)
W
(A) \( 4 \mathrm{R}^{2} \)
(B) \( 16 \mathrm{R}^{2} \)
(C) \( 32 \mathrm{R}^{2} \)
(D) \( 64 \mathrm{R}^{2} \)
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