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

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 by Tony 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 by mr 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 .

Facebook Tweet Pin