The triangle formed by joining the three excentres Ι 1 , Ι 2 and Ι 3 of Δ ABC is called the excentral or excentric triangle and in this case internal angle bisector of triangle ABC are the altitudes of triangles I 1 I 2 I 3
(i) Incentre Ι of Δ ABC is the ......... of the excentral Δ Ι 1 Ι 2 Ι 3 .
Text Solution
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(i) Clearly
(ii) Let ∠ Ι 3 Ι 1 Ι 2 = θ
Then angle of pedal trinagle = π – 2 θ = A
θ = 
(iii) Side of pedal triangle = I 2 I 3 cos θ = BC
I 2 I 3 = 
I 2 I 3 = 4Rcos 
(iv) Ι Ι 1 = 4 R sin 
I 2 I 3 = 4 R cos 
∴ ΙΙ 12 + Ι 2 Ι 32 = 16R 2
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