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The perpendicular from the centre of the circle to its chord, bisects the chord. So, AC = CB = (24/2) = 12 cm Similarly, DF = FE In right rAOC, using Pythagoras theorem, AO2 = AC2 + CO2 Or, 132 = 122 + CO2 So, CO2 = 169 - 144 = 25 Or, CO = √25 = 5 cm And, OF = CF - CO = 5 + 4√5 - 5 = 4√5 cm In right rDOF, using Pythagoras theorem, DO2 = DF2 + OF2 So, DF2 = 132 - (4√5)2 Or, DF2 = 169 - 80 = 89 So, DF = √89 cm DE = DF + FE = 2DF = 2√89 cm
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