Question

$\overline{ab}$ is a radius. $\overleftrightarrow{cd}$ is tangent to circle $a$ at point $b$, where $ab = 7$ and $ec = 18$.
what is $bc$?
enter your answer in the box.
$bc = \square$

Explanation:

Step1: Define variables

Let $BC = x$, $AE = AB = 7$ (radius), so $AC = AE + EC = 7 + 18 = 25$.

Step2: Use tangent-radius theorem

$\angle ABC = 90^\circ$, so apply Pythagoras: $AB^2 + BC^2 = AC^2$
$\Rightarrow 7^2 + x^2 = 25^2$

Step3: Solve for $x$

$49 + x^2 = 625$
$\Rightarrow x^2 = 625 - 49 = 576$
$\Rightarrow x = \sqrt{576} = 24$

Answer:

$24$