Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse \overline{AC}AC. If AD=9AD=9 and BD=3,BD=3, what is the length of \overline{DC}?DC?
+36 If in a right angled triangle ABC, the altitude h = BD from the right angle B to the hypotenuse AC divides the hypotenuse by segments of the length x and y, then
h2 = x*y. (1)
It is the general formula and the general statement/fact from Euclidean geometry. In our case h = BD = 3, x = AD = 9, and the problem asks about y = DC. From formula (1), y = h2/x = 32/9 = 9/9 = 1.
DC = 1.
