Question

A classmate insists that the value of x is 10. write an equation to show that your classmate is wrong and solve for x.

Answer 1

the complete question in the attached figure

we know that

If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.(Intersecting Secants Theorem)

5*(5+12)=6*(x+6)
5*17=6x+36
85=6x+36
6x=85-36
6x=49
x=49/6
x=8.17

the answer is
x=8.17