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In a given figure, AO/OC = DO/OB = 1/2 and AD = 4 cm. What is the length of BC?
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Solution: Step 1: Given ΔAOB similar to ΔCOD Step 2: AO/OC = DO/OB = 1/2 Step 3: AD = 4 cm Step 4: Using similarity, AO/OC = AB/CD Step 5: 1/2 = AB/CD Step 6: AB = (1/2)CD Step 7: AD = AB + BD = 4 cm Step 8: Since ΔAOB & ΔCOD are similar Step 9: AB/CD = 1/2 Step 10: Let CD = 2x, AB = x Step 11: x + 4 = 2x (as AD = AB + BD and BD = CD = 8) Step 12: x = 4, CD = 8 cm Step 13: Therefore, BC = 8 cm
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