neefd help fast

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- Jun 27th 2006, 02:48 PMAHDDMneed help in less than 3hrs circle
neefd help fast

http://img404.imageshack.us/img404/3...titled33ix.jpg - Jun 27th 2006, 07:20 PMSoroban
Hello, AHDDM!

We are given: $\displaystyle AD = 12$ and $\displaystyle DC - BD = 18\;\;\Rightarrow\;\; DC = BD + 18$

Let $\displaystyle BD = x$, then $\displaystyle DC = x + 18$

$\displaystyle \Delta ABC$ is inscribed in a semicircle.

. . Hence, $\displaystyle \Delta ABC$ is a right triangle.

$\displaystyle AD$ is the altitude to the hypotenuse of a right triangle.

Theorem: The altitude to the hypotenuse of a right triangle is

. . the mean proportional of the two segments of the hypotenuse.

Hence: .$\displaystyle x(x+18) \,=\,12^2$

We have the quadratic: .$\displaystyle x^2 + 18x - 144\:=\:0$

. . which factors: .$\displaystyle (x - 6)(x + 24) \:=\:0$

. . and has the positive root: .$\displaystyle x = 6$

Therefore: .$\displaystyle BD = 6,\;\;DC = 24\quad\Rightarrow\quad BC = 30$ cm.

- Jun 29th 2006, 10:25 PMAHDDM
thx 4 the reply

i keep frogetting to subtitute gotta learn to remeber