There is a moving point P in a triangle ABC of which sides are a,b,c and a>b>c find the minimum and maximum of AP+BP+CP


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Question Number 94144 by Tony Lin last updated on 17/May/20

$T h e r e i s a m o v i n g p o i n t P i n a t r i a n g l e$ $A B C o f w h i c h s i d e s a r e a, b, c a n d a > b > c$ $f i n d t h e m i n i m u m a n d m a x i m u m$ $o f A P + B P + C P$
Commented byTony Lin last updated on 17/May/20

$t h a n k s s i r I a l m o s t f o r g o t R = \frac{a b c}{4 Δ}$
Commented bymr W last updated on 17/May/20

$m i n i m u m = 3 R = \frac{3 a b c}{\sqrt{(a + b + c) (- a + b + c) (a - b + c) (a + b - c)}}$ $w h e n P i s t h e c i r c u m c e n t e r .$ $m a x i m u m = a + b$ $w h e n P i s t h e v e r t e x C .$
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