Question

Solve for x. Assume that lines that which appears to be tangent are tangent. This is geometry(:

Answer 1

Given:

Required:

To find the value of x.

Explanation:

The line that touches the circle is a tangent line.

We know that the line drawn from the centre of the circle to the tangent is perpendicular.

Thus the given triangle is the right angle triangle.

Where adjacent= 16

opposite = x

and hypotenuse = 8+x

Use the Pythagoras theorem:

$(hyp.)^2=(adj.)^2+(opp.)^2$$(x+8)^2=(16)^2+(x)^2$

Use the identity:

$(a+b)^2=a^2+2ab+b^2$$x^2+16x+64=256+x^2$

Solve by cancelling out the same term.

$\begin{gathered} 16x+64=256 \\ 16x=256-64 \\ 16x=192 \\ x=\frac{192}{16} \\ x=12 \end{gathered}$

Final answer:

The value of x=12