# need help in less than 3grs circle

• Jun 27th 2006, 02:48 PM
AHDDM
need help in less than 3hrs circle
• Jun 27th 2006, 07:20 PM
Soroban
Hello, AHDDM!

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

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

$\Delta ABC$ is inscribed in a semicircle.
. . Hence, $\Delta ABC$ is a right triangle.

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

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

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

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

Therefore: . $BD = 6,\;\;DC = 24\quad\Rightarrow\quad BC = 30$ cm.
• Jun 29th 2006, 10:25 PM
AHDDM
thx 4 the reply

i keep frogetting to subtitute gotta learn to remeber