LET A,B,C BE AN ACUTE ANGLED TRIANGLE AND LET D,E,F BE FEET OF PERPENDICULARS FROM A,B,C RESPECTIVELY TO BC,CA,AB.LET THE PERPENDICULARS FROM F TO CB,CA,AD,BE MEET THEM IN P,Q,M,N RESPECTIVELY.PROVE THAT P,Q,M,N ARE COLLINEAR ...
There are 24 equally spaced points lying on circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points and joining the three points of each set? ...
