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.
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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.
The two triangles have equal radii as corresponding sides and equal chord lengths as their bases. Therefore, all three corresponding sides are equal, so the triangles are congruent by the SSS Congruence Criterion.
The two sides joining the centre to the endpoints of the chord are radii of the same circle. Since all radii are equal, the triangle formed is an isosceles triangle.