Mathematics
In an equilateral triangle, prove that the centroid and the circumcentre of the triangle coincide.
Related Questions
If a diameter of a circle is perpendicular to one of two parallel chords of the circle, prove that it is perpendicular to the other and bisects it.
In the figure (ii) given below, O is the center of a circle. If AB and AC are chords of the circle such that AB = AC and OP ⊥ AB, OQ ⊥ AC, prove that PB = QC.
The line joining mid-points of two chords of a circle passes through its center. Prove that the chords are parallel.
In the figure (i) given below, OD is perpendicular to the chord AB of a circle whose center is O. If BC is a diameter, show that CA = 2OD.
