Circles And Geometry

Step 1: Use the chord length and perpendicular distance.
For any circle, the perpendicular from the center of the circle to a chord bisects the chord. Thus, if the length of the chord is and the distance from the center is , the radius of the circle can be found using the Pythagorean theorem: We are given that the length of the first chord is 6 cm and its perpendicular distance from the center is 4 cm. For this chord, we have:

Step 2: Use the radius for the second chord.
Now, for the second chord, we have a chord length of 8 cm, so and . Using the Pythagorean theorem again, the distance from the center is :

Step 3: Conclusion.
The correct answer is (C) 3.5 cm.