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The triangle formed by ioining the three excentres \( \mathbf{I}_{\mathbf{1}} \mathbf{I}_{\mathbf{2}} \) and \( \mathbf{I}_{\mathbf{3}} \) 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 \( \mathrm{I}_{1} \mathrm{I}_{2} \mathrm{I}_{3} \)
\( \mathrm{P} \)
Angles of the \( \Delta I_{1} I_{2} I_{3} \) are
W
(A) \( \frac{\pi}{2}-\frac{\mathrm{A}}{2}, \frac{\pi}{2}-\frac{\mathrm{B}}{2} \) and \( \frac{\pi}{2}-\frac{\mathrm{C}}{2} \)
(B) \( \frac{\pi}{2}+\frac{A}{2}, \frac{\pi}{2}+\frac{B}{2} \) and \( \frac{\pi}{2}+\frac{C}{2} \)
(C) \( \frac{\pi}{2}-A, \frac{\pi}{2}-B \) and \( \frac{\pi}{2}-C \)
(D) None of these
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