Problem:
In â–³ABC, we have AC=BC=7 and AB=2. Suppose that D is a point on line AB such that B lies between A and D and CD=8. What is BD?
Answer Choices:
A. 3
B. 23​
C. 4
D. 5
E. 42​
Solution:
Let CH be an altitude of â–³ABC. Applying the Pythagorean Theorem to â–³CHB and to â–³CHD produces
82−(BD+1)2=CH2=72−12=48, so (BD+1)2=16
Thus BD=3.
Answer: A​.
The problems on this page are the property of the MAA's American Mathematics Competitions
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