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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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.
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.
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 least possible radius is obtained when the two given points are the endpoints of the diameter of the circle. Therefore, the smallest radius equals half the distance between the two points.