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    OlympiadMediumGeometry7–9

    Two circles of radius 55 cm have centres 66 cm apart. How long is their common chord, in cm?

    Duas circunferências de raio 55 cm têm os centros a 66 cm de distância. Qual é o comprimento da corda comum, em cm?

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    Solution

    The line of centres cuts the chord at right angles and, since the radii are equal, cuts it at the midpoint of the 66 cm gap. Half the chord is 52−32=4\sqrt{5^{2} - 3^{2}} = 4, so the chord is 88 cm.