let-C-a-r-z-C-z-a-r-Let-u-v-w-C-a-r-such-as-u-v-2w-Prove-that-u-a-v-a-1-u-v-w-It-shows-that-the-middle-of-a-segment-joining-two-points-in-a-circle-is-not-in-that-circle-

Tinku Tara June 3, 2023 Integration 0 Comments

Question Number 136762 by snipers237 last updated on 25/Mar/21

let C(a,r)={z∈C, ∣z−a∣=r } Let u,v,w ∈C(a,r) such as u+v=2w Prove that ((u−a)/(v−a)) =1 , u=v=w It shows that the middle of a segment joining two points in a circle is not in that circle

$$\:{let}\:\:{C}\left({a},{r}\right)=\left\{{z}\in\mathbb{C},\:\:\mid{z}−{a}\mid={r}\:\right\} \\ $$$${Let}\:{u},{v},{w}\:\in{C}\left({a},{r}\right)\:{such}\:{as}\:\:\:{u}+{v}=\mathrm{2}{w} \\ $$$${Prove}\:{that}\:\:\frac{{u}−{a}}{{v}−{a}}\:=\mathrm{1}\:,\:{u}={v}={w} \\ $$$$ \\ $$$${It}\:{shows}\:{that}\:{the}\:{middle}\:{of}\:{a}\:{segment}\: \\ $$$${joining}\:{two}\:{points}\:{in}\:{a}\:{circle}\:\:{is}\:{not}\:{in}\:{that}\:{circle} \\ $$

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let-C-a-r-z-C-z-a-r-Let-u-v-w-C-a-r-such-as-u-v-2w-Prove-that-u-a-v-a-1-u-v-w-It-shows-that-the-middle-of-a-segment-joining-two-points-in-a-circle-is-not-in-that-circle-

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