Equal perpendicular distances from the centre imply that the two chords are equidistant from the centre. By Theorem 7, chords equidistant from the centre of a circle are equal. Therefore, AB = GF.
Consider Fig. 5.15. If CE is perpendicular to AB, CH is perpendicular to GH, and CE = CH, show that AB = GF.
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Since CE and CH are perpendicular distances from the centre to the chords and CE = CH, both chords are at the same distance from the centre. According to Theorem 7, chords that are equidistant from the centre of the same circle are equal in length. Hence, the two chords are equal. Therefore, AB = GF.
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