Two circles have equal radii of 7cm with centres O1 and O2 respectively.
In the first circle, chord AB measures 8cm and in the second circle, chord CD also measures 8cm.
The line O1O2 equals 20cm. Answer the following questions.
(i) Prove that ∠AO1B=∠CO2D.
(ii) Will the equality of AB and CD guarantee equal central angles if the radii of the two circles are not equal? Give a clear reason for your answer.
(iii) Suppose the radius of the second circle is changed to 9cm while chord CD remains 8cm. State whether ∠CO2D is greater than, equal to, or less than ∠AO1B and justify your answer without using trigonometry.