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.
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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.
The perpendicular distances of the two chords from the centre are found using the Pythagoras Theorem. Since the chords lie on opposite sides of the centre, the required distance is the sum of these distances, which is seven centimetres.
In an isosceles triangle, the altitude from the vertex bisects the base. The perpendicular bisector of a chord passes through the centre of the circle. Therefore, the altitude passes through the centre.
The two right triangles have equal radii as hypotenuses and a common perpendicular side. Therefore, they are congruent by the RHS Congruence Criterion. Hence, the chord is divided into two equal parts.