- Sneha Titus
- 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 guide you to visualize the locus:
(i) AB is a chord of the circle with centre O, M is the mid-point of the chord. What is angle OMB? Will angle OMB change as B moves around the circle? Experiment with GeoGebra and make a conjecture about angle OMB.
(ii) What about angle OMA?
(iii) Can you now predict the locus of M?
Move the point B around the circle, the locus of M will be traced out simultaneously. Is this the locus you predicted?
Justify your stance. Hint: You will need to know a theorem about the angle in a semi-circle.