The perpendicular from the centre bisects the chord, forming two right triangles. Applying the Baudhāyana–Pythagoras Theorem gives the half-chord as √(r² − d²). Hence, the chord length is 2√(r² − d²).
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Using the chord-length formula or the Baudhāyana–Pythagoras Theorem, the half-chord measures √13 cm. Therefore, the complete chord length is 2√13 cm.
Apply the Baudhāyana–Pythagoras Theorem to the right triangles formed by the radii and perpendiculars. Equal radii and equal perpendicular distances give equal half-chords. Hence, the complete chords are equal.
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.
Using the Baudhāyana–Pythagoras Theorem, equal chords with equal radii give equal perpendicular distances from the centre. Hence, chords of equal length are always equidistant from the centre of the circle.