let ABC be a triangle with incenter I. prove that Ia . Ib . Ic ≤ ((abc)/8)


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Question Number 218393 by Nicholas666 last updated on 09/Apr/25

$l e t A B C b e a t r i a n g l e w i t h i n c e n t e r I .$ $p r o v e t h a t I a . I b . I c ⩽ \frac{a b c}{8}$
	Answered by mr W last updated on 13/Apr/25

	$s e e m s w r o n g!$ $e x a m p l e : a = b = c$ $I A = I B = I C = \frac{a}{\sqrt{3}}$ $I A \cdot I B \cdot I C = {(\frac{a}{\sqrt{3}})}^{3} = \frac{a^{3}}{3 \sqrt{3}} ⩽ \frac{a b c}{8}$
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