SOLUTION: the radii of 2 concentric circles are 13 cm and 8 cm.AB is a diameter of bigger circle.BD is a tangent of the smaller circle touching it at D. find the length of AD.

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Question 720934: the radii of 2 concentric circles are 13 cm and 8 cm.AB is a diameter of bigger circle.BD is a tangent of the smaller circle touching it at D. find the length of AD.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Let the common center of the two circles be O



Draw OD.  Then  OD⊥BD because radius OD drawn to the point of tangency is
perpendicular to the tangent line BD.

so ߡOBD is a right triangle with hypotenuse OB.

cos(∠DOB) = OD%2FOB = 8%2F13

cos(∠AOD) = cos(180°-∠DOB) = -cos(∠DOB) = -8%2F13 



Use the law of cosines:

ADČ = AOČ + ODČ - 2·AB·OD·cos(∠AOD)

ADČ = 13Č + 8Č - 2·13·8·%28-8%2F13%29

ADČ = 169 + 64 + 128

ADČ = 361

AD = √361

AD = 19.

Edwin