SOLUTION: Let B, C, and D be points on a circle. Let BC and the tangent to the circle at D intersect at A. If AB = 4, AD = 8, and AC is perpendicular to AD, then find CD. https://latex.ar

The key to the solution of the problem is this theorem


     Theorem

     If a tangent and a secant lines are released from a point outside a circle, 
     then the product of the measures of the secant and its external part is equal to the square of the tangent segment.


For the proof, see the lesson

    - Metric relations for a tangent and a secant lines released from a point outside a circle

in this site.


Using the theorem, you can find the length of the secant AC:  |AC| =  =  =  = 16 units.


Then |CD| =  =  = .