- Point P is on a circle with center O.
- Length OP = 3.5 units.


Which of the given segment lengths can be the chord of the circle.



- A chord is a line segment that connects two points on a circle.
- The length of a chord is the distance between the two points.


- We need to check if the given segment lengths can be the length of a chord.
- To do this, we can use the theorem that states "In a circle, a perpendicular drawn from the center of the circle to a chord bisects the chord."
- If the given segment length is less than or equal to the distance between the center and the point where the perpendicular bisects the chord, then it can be the length of a chord.


- Let's assume the given segment lengths as the distance between the center and the point where the perpendicular bisects the chord.
- To find the distance, we can use the Pythagorean theorem.
- The distance can be calculated as follows:

Distance = sqrt(OP^2 - half_chord^2)


1. 8 cm:
- Distance = sqrt(3.5^2 - 8^2/4) = sqrt(12.25 - 16) = sqrt(-3.75).
- Since the distance is imaginary, 8 cm cannot be the length of a chord.

2. 5 cm:
- Distance = sqrt(3.5^2 - 5^2/4) = sqrt(12.25 - 6.25) = sqrt(6).
- The distance is a real number, so 5 cm can be the length of a chord.

3. 8.5 cm:
- Distance = sqrt(3.5^2 - 8.5^2/4) = sqrt(12.25 - 36.125) = sqrt(-23.875).
- Since the distance is imaginary, 8.5 cm cannot be the length of a chord.

4. 9 cm:
- Distance = sqrt(3.5^2 - 9^2/4) = sqrt(12.25 - 20.25) = sqrt(-8).
- Since the distance is imaginary, 9 cm cannot be the length of a chord.


- Based on the calculations, the only segment length that can be the length of a chord is 5 cm. The other lengths (8 cm, 8.5 cm, and 9 cm) cannot be the lengths of chords.