Final answer:
The radius of the circle is found to be 6 cm by using the Pythagorean theorem on the right triangle formed by the radius, tangent, and the distance from the point of tangency to the external point.
Step-by-step explanation:
The student is asking about the relationship between the length of a tangent to a circle, the distance from the point of tangency to an external point, and the radius of the circle. According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Since a tangent to a circle is perpendicular to the radius at the point of tangency, we can form a right triangle with the radius as one leg, the length of the tangent as another, and the distance from the external point to the center of the circle as the hypotenuse.
In this case, the distance from the external point to the center of the circle is given as 10 cm (the hypotenuse), and the length of the tangent is given as 8 cm. Let r be the radius of the circle. The Pythagorean theorem then gives us:
r2 + 82 = 102
r2 + 64 = 100
r2 = 100 - 64
r2 = 36
r = 6 cm
Therefore, the radius of the circle is 6 cm, which corresponds to option (c).