Mathematics 2009 JAMB Past Questions - Question 31: What is the locus of the mid point of all chords of length 6cm with a circle of radius 5cm and with center 0.

Correct Answer

C

Explanation

The locus of the midpoint of all chords of length 6 cm in a circle with a radius of 5 cm and center at (0,0) is a circle.To see why, let's consider any chord of length 6 cm in the circle. The midpoint of this chord will lie on the perpendicular bisector of the chord. Since the chord has a fixed length of 6 cm, the perpendicular bisector will always be equidistant from the endpoints of the chord.Now, let's consider all possible chords of length 6 cm in the circle. The perpendicular bisectors of these chords will intersect at the center of the circle (0,0). Therefore, the locus of the midpoints of all these chords will be the circle with center (0,0) and radius equal to half the length of the chords, which is 3 cm.Hence, the locus of the midpoint of all chords of length 6 cm in the given circle is a circle with center (0,0) and radius 3 cm.