Question 45
LociWhat is the locus of the mid-points of all chords of length 6cm within a circle of radius 5cm and with centre O?
- A.A circle of radius 4cm and with centre O
- B.The perpendicular bisectors of the chords
- C.A straight line passing through centre O
- D.A circle of radius 6cm and with centre O
Show the answer and explanation
Answer: A (A circle of radius 4cm and with centre O)
Explanation
The midpoint of each chord is √(5² − 3²) = 4cm from O. So all the midpoints lie on a circle of radius 4cm centred at O.