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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.

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#### 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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