Question

Find the value of $x=BC$ from the following figure :

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is C $4$

Given, $BC=x$

Also we have from figure, $AB=12$

$BC=x$, $BD=9x$

Thus $BC+CD=9x$

$\Rightarrow x+CD=9x$

$\Rightarrow CD=8x$

Using the secant intersection theorem, we have

${\left(AB\right)}^2=BC(BC+CD)\Rightarrow {\left(12\right)}^2=x(x+8x)\Rightarrow 9x^2=144\Rightarrow x^2=\frac{144}{9}=16\Rightarrow x=4$

So, option C is correct