Question

Anybody have the answer to this?

Answer 1

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.

$x^2 + (13.5)^2 = (x + 8.45)^2$

$x^2 + 182.85 = x^2 + 16.9x + 71.4025$

$182.25 = 16.9x + 71.4025$

$-16.9x = -110.8475$

$x = 6.559$

Answer: x = 6.6 cm