Two concentric circles have radius of 6mm and 12mm. a segment tangent to the smaller circle is a chord to the larger circle. what is the length of the segment to the nearest tenth?

The length of the segment is  12√3

Explanation:

We are given radius of inner circle = 6mm and that of outer circle = 12mm and chord of outer circle is tangent to inner circle

The point of intersection (consider T) of tangent to inner circle divides the chord (say AB) into two parts

let center = O , so radius of inner and outer circle and half the chord form a right angled triangle (say AOT)

where OT is perpendicular to AT.

We have OT = 6mm and OA = 12mm ,

applying pythagoras theorem we get

AT*AT = OA*OA - OT*OT

AT*AT = 144-36 = 108,

AT = 6√3

which gives AB = 2*AT

                       = 2*6√3

                        =12√3 which is the length of the segment

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!