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Διερευνώντας την εγγραψιμότητα σε κύκλο

Έχουμε αποδείξει ότι μία ευθεία κι ένας κύκλος έχουν το πολύ δύο κοινά σημεία. Επίσης οποιαδήποτε δύο σημεία ορίζουν μοναδική ευθεία.
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[/img]

Δοθέντων δύο σημείων του επιπέδου μπορείτε να κατασκευάσετε έναν κύκλο που να διέρχεται από αυτά τα σημεία; Περιγράψτε την κατασκευή και δημιουργήστε την στο επόμενο πλαίσιο.

Κατασκευάστε έναν κύκλο που διέρχεται από τα σημεία Α και Β παρακάτω:

Πόσους διαφορετικούς τέτοιους κύκλους μπορείτε να κατασκευάσετε; Ποιες οι προϋποθέσεις για την κατασκευή;

Κατασκευάστε έναν κύκλο, οποίος να διέρχεται από τα επόμενα τρία σημεία.

Πόσους διαφορετικούς κύκλους μπορείτε να κατασκευάσετε, οι οποίοι να διέρχονται από τα τρία παραπάνω σημεία;

Αν τα σημεία γίνουν συνευθειακά πόσους κύκλους μπορείτε να κατασκευάσετε;

Κατασκευάστε έναν κύκλο, ο οποίος, αν γίνεται, να διέρχεται και από τα τέσσερα επόμενα σημεία.

Ποιες οι προϋποθέσεις για την κατασκευή; Καταγράψτε παρακάτω όσα περισσότερα κριτήρια μπορέσετε να διαμορφώσετε.

Συνοψίζοντας...μία άλλη επέκταση. Διερεύνηση τεσσάρων σημείων και σφαίρας

Συνοψίζοντας έχουμε: * Από δύο διαφορετικά σημεία διέρχεται μοναδική ευθεία. * Από δύο διαφορετικά σημεία διέρχονται άπειροι κύκλοι, όλοι όσοι έχουν κέντρο στη μεσοκάθετο του ευθυγράμμου τμήματος με άκρα αυτά τα σημεία. * Από τρία διαφορετικά σημεία διέρχεται μοναδικός κύκλος, εφόσον αυτά είναι μη συνευθειακά. * Μπορούμε να κατασκευάσουμε σφαίρα, η οποία να διέρχεται από τρία σημεία; Περισσότερες από μία; * Πόσα σημεία χρειαζόμαστε για να κατασκευάσουμε μοναδική σφαίρα;