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Question

In ABC, 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?

Accepted Answer

Let CH be an altitude of ABC. Applying the Pythagorean Theorem to CHB and to CHD produces 8^2 - (BD +1)^2 = CH^2 = 7^2 - 1^2 = 48, so (BD+1)^2 = 16. Thus BD = 3. FIGURE