Q24 of 180 Page 1

In the given figure, the radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle and BD is a tangent to the smaller circle touching it at D. Find the length of AD.


In the given diagram,


AB = 13 cm, OD = 8 cm


⇒ OD ⊥ BE [Radii of a circle is perpendicular to the tangent at the point of contact]


Using Thales theorem, if three points A, B, E lies on a circle, and AB is the diameter, then ∠AEB = 90°


⇒ ∠AEB = ∠ODB = 90°


⇒ O is the midpoint of AB and D is the midpoint of BE.


⇒ AE = 2 × OD = 16 cm.


In triangle, OBD


Using Pythagoras theorem,


⇒


⇒


⇒


But BD = DE


Again, using Pythagoras theorem in ADE


⇒


⇒


⇒


Hence, the required answer is 19 cm.


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