Equal chords and their distances from the centre

作者:
Healey Lee
Objective: To explore the relationship between equal chords and their distances from the centre of the circle. The figure shows a circle of centre O with two equal chords AB and CD (i.e. the lengths of AB and CD are equal). M and N are points on chords AB and CD respectively such that OM⊥AB and ON⊥CD.
1. Drag point A to point C. Are the lengths of OM and ON equal? 2. Check the result of question 1 by pressing the button . 3. Vary the length of chord AB (CD) by dragging point X on the scroll bar. Then, repeat the steps in questions 1 and 2. For two equal chords, what is the relationship between their distances from the centre of the circle? 4. If chords AB and CD are not equal chords, is the relationship in question 3 still hold? Verify your conjecture by drawing a circle with two unequal chords.