The length of line shown in the figure below is 16cm and the radius of the circle is 10cm. Calculate the length from the center of the line to the center of the circle.
To find the length from the center of the line to the center of the circle, we can draw a line perpendicular to the line from the center of the circle. This line will intersect the line at the center of the line segment.
Since the line segment is bisected by the center of the circle, the distance from the center of the line to the intersection point will be half the length of the line segment, which is 8 cm.
Now, we have a right triangle with one leg of length 8 cm and the hypotenuse of the triangle is the radius of the circle, which is 10 cm. We can use the Pythagorean theorem to find the other leg of the triangle:
a^2 + b^2 = c^2
8^2 + b^2 = 10^2
64 + b^2 = 100
b^2 = 100 - 64
b^2 = 36
b = √36
b = 6
Therefore, the length from the center of the line to the center of the circle is 6 cm.