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-

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

l e t C (a, r) = {z \in C, ∣ z - a ∣= r}

L e t u, v, w \in C (a, r) s u c h a s u + v = 2 w

P r o v e t h a t \frac{u - a}{v - a} = 1, u = v = w

I t s h o w s t h a t t h e m i d d l e o f a s e g m e n t

j o i n i n g t w o p o i n t s i n a c i r c l e i s n o t i n t h a t c i r c l e