A) 6 cm
B) 8 cm
C) 10 cm
D) 12 cm
The distance of the chord from the center of the circle is B) 8 cm.
Here’s why:
- Draw the diagram: Imagine a circle with a radius of 10 cm. Draw a chord within the circle with a length of 12 cm. From the center of the circle (O), draw a line perpendicular to the midpoint of the chord (let’s call this point L).
- Identify key features: This perpendicular line (OL) divides the chord into two equal halves (since the perpendicular drawn from the center of a circle to a chord bisects the chord). Therefore, each half of the chord will be 12 cm / 2 = 6 cm.
- Apply the Pythagorean Theorem: Now we have a right triangle (△OAL) where OA (radius) is the hypotenuse (10 cm), AL (half of the chord) is one leg (6 cm), and OL (distance from the center to the chord) is the other leg. We can use the Pythagorean theorem:
- OL^2 = OA^2 – AL^2
- OL^2 = (10 cm)^2 – (6 cm)^2
- OL^2 = 100 cm^2 – 36 cm^2
- OL^2 = 64 cm^2
- Taking the square root of both sides: OL = √64 cm = 8 cm
Therefore, the distance of the chord from the center of the circle is 8 cm.