![In an equilateral triangle, prove that the centroid and centre of the circum-circle (circum centre) coincide). In an equilateral triangle, prove that the centroid and centre of the circum-circle (circum centre) coincide).](https://doubtnut-static.s.llnwi.net/static/web-thumb/642572681_web.png)
In an equilateral triangle, prove that the centroid and centre of the circum-circle (circum centre) coincide).
![Investigate the pedal triangle when the Pedal Point, P, is the centroid for equilateral triangle ABC. Investigate the pedal triangle when the Pedal Point, P, is the centroid for equilateral triangle ABC.](http://jwilson.coe.uga.edu/EMAT6680Fa10/Gammaro/Assignment9/A9_%20Pedal_Triangles/Assignment%209%20%E2%80%93%20Pedal%20Triangles_files/image012.png)
Investigate the pedal triangle when the Pedal Point, P, is the centroid for equilateral triangle ABC.
![Investigate the pedal triangle when the Pedal Point, P, is the centroid for equilateral triangle ABC. Investigate the pedal triangle when the Pedal Point, P, is the centroid for equilateral triangle ABC.](http://jwilson.coe.uga.edu/EMAT6680Fa10/Gammaro/Assignment9/A9_%20Pedal_Triangles/Assignment%209%20%E2%80%93%20Pedal%20Triangles_files/image008.png)
Investigate the pedal triangle when the Pedal Point, P, is the centroid for equilateral triangle ABC.
![Investigate the pedal triangle when the Pedal Point, P, is the centroid for equilateral triangle ABC. Investigate the pedal triangle when the Pedal Point, P, is the centroid for equilateral triangle ABC.](http://jwilson.coe.uga.edu/EMAT6680Fa10/Gammaro/Assignment9/A9_%20Pedal_Triangles/Assignment%209%20%E2%80%93%20Pedal%20Triangles_files/image010.png)