Circling Around
Problem Statement
- A is a fixed point on a given circle, and B is a variable point on the circle; it travels around the circle. M is the midpoint of AB. What is the locus of M?
Questions that can help you find the locus
AB is a chord of the circle with centre O, M is the mid-point of the chord. What is angle OMB? Will the value of angle OMB change as B moves around the circle? Experiment with GeoGebra and make a conjecture about angle OMB. Justify your conjecture.
(iii) Can you now predict the locus of M?
Move the point B around the circle, then redefine your conjecture if you want.
Click on the check box to see the locus.
Is this the locus you predicted?
Justify your stance. Hint: You will need to know a theorem about the angle in a semi-circle.