Answer:
x=6.5 cm
Step-by-step explanation:
The tangent meets the circle at right angles.
Therefore the triangle formed is a right triangle.
From the Pythagorean Theorem;
[tex]x^{2} +20.2^2=(x+14.7)^2[/tex]
We expand to obtain:
[tex]x^{2} +408.4=x^2+29.4x+216.04[/tex]
We group like terms to get:
[tex]x^{2} -x^2+408.4-216.04=29.4x[/tex]
We simplify now to get:
[tex]192.36=29.4x[/tex]
We divide both sides by 29.4 to get:
x=6.5 to the nearest tenth.
