What is the length of the radius of a circle with center (10, -14) that is tangent to the line x=13?

The length of the radius of a circle as described in the question is; 14.32

The center of the circle is at; (10, -14)

The line that is tangent to the circle is; x = 13.

The coordinate of a point on the line is therefore; (13, 0)

The length of the radius of the circle can.be obtained from Pythagoras theorem as;

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length of radius of a circle = 3

Step-by-step explanation:

a tangent line touches the circle at one point

if the tangent line is at x=13 (vertical line) and the center of the circle is

(x,y) = (10,-14) with its center x at 10; then take the difference to find the radius;

x(tangent line) - x(center of circle) = radius of circle

length of radius of a circle = 13-10 = 3

you can also graph the circle and draw the tangent line to find the radius

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

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step-by-step explanation: