6-of-the-23-given-points-in-the-plane-lie-on-a-circle-Let-n-be-the-number-of-circles-passing-through-at-least-3-of-these-points-What-is-the-maximum-number-of-n-

Question Number 183366 by Shrinava last updated on 25/Dec/22

$$\mathrm{6}\:\mathrm{of}\:\mathrm{the}\:\mathrm{23}\:\mathrm{given}\:\mathrm{points}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{lie}\:\mathrm{on}\:\mathrm{a}\:\mathrm{circle}.\:\mathrm{Let}\:\boldsymbol{\mathrm{n}}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{circles}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{of} \\ $$$$\mathrm{these}\:\mathrm{points}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{number}\:\mathrm{of}\:\boldsymbol{\mathrm{n}}? \\ $$

Commented by mr W last updated on 25/Dec/22

$${at}\:{least}\:\mathrm{3}\:{of}\:{these}\:{points}?\: \\ $$$${are}\:{these}\:{points}\:{the}\:\mathrm{6}\:{special}\:{points}\: \\ $$$${or}\:{all}\:{the}\:\mathrm{23}\:{points}? \\ $$

Commented by Shrinava last updated on 25/Dec/22

$$\mathrm{23}\:\mathrm{dear}\:\mathrm{professor} \\ $$

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