Given that P and Q are points on the sides AB and AC respectively of . The perpendiculars to the sides AB and AC at P and Q respectively meet at D, an interior point of . If M is the midpoint of BC, prove that PM = QM if and only if .

Let . Written in the usual decimal form, find the last two digits of the number N. SOLUTION:here

Two circles and having centers at and intersect at A and B. Let P be a point on the segment AB and let . The line through P perpendicular to meets at C and D. The line through P perpendicular to meets at E and F. prove that C,D, E and F form a rectangle. SOLUTION: here

Solve the equation for positive integers x, y. SOLUTION: here

From the list of natural numbers 1, 2, 3, … suppose we remove all multiples of 7, all multiples of 11 and all multiples of 13.

At which position in the resulting list does the number 1002 appear?

What number occurs in the position 3600? SOLUTION:here

sir solution for 5th problem

can you give solution for other problems too?waiting in anticipation.