Question

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

Answer 1

20.8 If you actually draw the described circles and the chord, you'll realize that you have two congruent right triangles of which you know the hypotenuse and leg and that the unknown leg is half the length of the desired chord. So you can use the Pythagorean theorem to calculate the 2nd leg and simply double that result to get the desired answer. So X = 2*sqrt(12^2 - 6^2) X = 2*sqrt(144 - 36) X = 2*sqrt(108) X = 2*sqrt(3*36) X = 6*2*sqrt(3) X = 12*sqrt(3) X = 12*1.732050808 X = 20.78460969 X = 20.8