I assume that the segment that measures 13.5 cm is a tangent to the circle at the point we see. The side that measures x is a radius of the circle, so the side of the triangle that measures x and the side that measures 13.5 cm are perpendicular. The triangle is a right triangle.
One leg measures x.
One leg measures 13.5 cm.
The hypotenuse measures x + 8.45 cm.
With the lengths of the the 3 sides, we can use the Pythagorean theorem and solve for x.
[tex] x^2 + (13.5)^2 = (x + 8.45)^2 [/tex]
[tex] x^2 + 182.85 = x^2 + 16.9x + 71.4025 [/tex]
[tex] 182.25 = 16.9x + 71.4025 [/tex]
[tex] -16.9x = -110.8475 [/tex]
[tex] x = 6.559 [/tex]
Answer: x = 6.6 cm
