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:
[tex](hyp.)^2=(adj.)^2+(opp.)^2[/tex][tex](x+8)^2=(16)^2+(x)^2[/tex]
Use the identity:
[tex](a+b)^2=a^2+2ab+b^2[/tex][tex]x^2+16x+64=256+x^2[/tex]
Solve by cancelling out the same term.
[tex]\begin{gathered} 16x+64=256 \\ 16x=256-64 \\ 16x=192 \\ x=\frac{192}{16} \\ x=12 \end{gathered}[/tex]
Final answer:
The value of x=12
