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.
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-> 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.
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Question 1074109: 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.artofproblemsolving.com/5/4/7/547ab841560cd28dd3d03fb5510dd297b29e8a42.png Answer by ikleyn(52754) (Show Source):
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| = = = .
