Carcass wrote:
Segment AC is the diameter of circle O with the length 10, and AB = 5. Segment BD is the altitude drawn from B to AC. What is the length of BD?
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(A) 5
(B) 5√3/2
(C) 2√10
(D) 3√5
(E) 3√10
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GRE Circle and triangle.jpg [ 16.33 KiB | Viewed 1223 times ]
Applying Pythagoras Theorem in \(ΔABC\);
\(AC^2 = AB^2 + BC^2\)
\(10^2 = 5^2 + BC^2\)
\(100 - 25 = BC^2\)
\(BC = \sqrt{75} = 5\sqrt{3}\)
Now, Area of \(ΔABC\) = \(\frac{1}{2}(AB)(BC)\) = \(\frac{1}{2}(AC)(BD)\)
\((AB)(BC) = (AC)(BO)\)
\((5)(5\sqrt{3}) = (10)(BD)\)
\(BD = \frac{5\sqrt{3}}{2}\)
Hence, option B