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Question
Two concentric circles with center O have A, B, C, D as the points of intersection with the lines L shown in the figure. If AD = 12 cm and BC s = 8 cm, find the lengths of AB, CD, AC and BD.
Solution
Since, OM ⊥ BC
BM = CM = `1/2`BC = 4 cm
also, OM ⊥ AD
So, AM = DM = `1/2` AD = 6 cm
now, AB = AM - BM = ( 6 - 4 ) cm = 2 cm
CD = DM - CM = ( 6 - 4 ) cm = 2 cm
∴ AC = AB + BC = ( 2 + 8 ) cm = 10 cm
and BD = BC + CD = ( 8 + 2 ) cm = 10 cm
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