A regular octagon and its red centre. Prove that the centres of the two circles lie on the semicircle.
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Solution
I is the center of the octagon. J is the center of big circle. K is the center of small circle. AB is the diameter of the semicircle. Since ∠AJB = 90° and ∠AKB = 90°, then J and K lies on the semicircle.
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