Final answer:
To construct a tangent to a circle with a radius of 4 cm from a point on a concentric circle with a radius of 6 cm, the length of the tangent is undefined.
Step-by-step explanation:
To construct a tangent to a circle, you need to draw a line that touches the circle at exactly one point. In this case, the circle has a radius of 4 cm and is concentric with another circle with a radius of 6 cm. The length of the tangent can be found using the Pythagorean theorem.
The distance between the centers of the two circles is the difference between their radii, which is 6 - 4 = 2 cm. This distance is the hypotenuse of a right triangle formed by the centers of the circles, the tangent point, and the foot of the perpendicular dropped from the center of the larger circle to the tangent. The perpendicular dropped from the center of the larger circle to the tangent is equal to the radius of the smaller circle, which is 4 cm.
Using the Pythagorean theorem, we can find the length of the tangent as follows: Length of tangent = √(Hypotenuse^2 - Perpendicular^2) = √(2^2 - 4^2) = √(4 - 16) = √(-12).
Since we can't take the square root of a negative number, the length of the tangent is undefined in this case.