Question

Hi, my son just started virtual learning and school not providing much help so far. Need help with step by step (show work) with these 4 problems to double check homework…x= (guess I can only ask one per time?! New to this…

Answer 1

Solution

Step 1

Use the secant and tangent theorem to a circle.

Step 2

AC = 30 + x

BC = x

CD = 20

Step 3

Substitute into the theorem

$\begin{gathered} (30+x)\times x\text{ = 20}^2 \\ \\ x^2+30x\text{ = 400} \\ \\ x^2+30x-400=0 \end{gathered}$

Step 4

Use the factorization method to solve for x.

$\begin{gathered} x^2+30x-400=0 \\ \\ x^2-10x+40x-400=0 \\ \\ x(x-10)+40(x-10)=0 \\ \\ (x+40)(x-10)=0 \\ \\ x-10=0,\text{ x+40=0} \\ \\ x\text{ = 10, x = -40} \end{gathered}$

Step 5

The value of x cannot be negative, hence x = 10

Final answer

x = 10