[list=1]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?[br][br][/list][br][br]
AB is a chord of the circle with centre O, M is the mid-point of the chord. What is angle OMB? [br]Will the value of angle OMB change as B moves around the circle? Experiment with GeoGebra and make a [br]conjecture about angle OMB.[br]Justify your conjecture.[br][br][br][br][br][br]
OM is perpendicular to AB as M is the mid-point of the chord. [br]Angle OMB is always 90 degrees
(iii) Can you now predict the locus of M? [br][br][br]
[br]Move the point B around the circle, then redefine your conjecture if you want.[br]Click on the check box to see the locus. [br]Is this the locus you predicted?[br][br][br]
Justify your stance. [br]Hint: You will need to know a theorem about the angle in a semi-circle.
Since angle OMB is always 90 degrees, the locus of M is a circle with diameter OA. Angle OMB is the angle in the semi-circle.