Question-17886

Question Number 17886 by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17

Commented by b.e.h.i.8.3.417@gmail.com last updated on 12/Jul/17

1) c i r c l e r a d i u s = R

2) a c u t e a n g l e b e t w e e n c h o r d s : A B, C D = φ

f i n d : {A P}^{2} + {B P}^{2} + {C P}^{2} + {D P}^{2} .

(i n t e r m s o f : R a n d φ)

t r i a l c a s e :

w h e n : φ = 90^{∙}

\Rightarrow {A P}^{2} + {B P}^{2} + {C P}^{2} + {D P}^{2} = 4 R^{2}

Commented by ajfour last updated on 12/Jul/17

what if the chord lengths have a

constant ratio k and acute ∠

between them is ϕ, with radius R ?

Commented by mrW1 last updated on 12/Jul/17

Commented by mrW1 last updated on 12/Jul/17

{A P}^{2} + {B P}^{2} + {C P}^{2} + {D P}^{2} is not constant

for a given φ, so you can not express it

in terms of R and φ . the case φ = 90 ° is an

exception .

See examples :

Commented by ajfour last updated on 12/Jul/17

i meant AB = k (CD) .

Commented by b.e.h.i.8.3.417@gmail.com last updated on 12/Jul/17

m r A j f o u r! h a v e y o u a n y s o l u t i o n f o r t h i s c a s e ?

Commented by ajfour last updated on 13/Jul/17

i think even in this question will not

fetch unique answers, given ϕ, R,

and k . Both chord lengths and ϕ

and R are required . See Q . 17963 . .

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