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Problem of the Week

Let T be an external point for the acute-angled ▲ABC and the sections MN, PQ, KL are parallel to the sides AB, BC, CA and they pass trough the point T and their ends are on the sides of the triangle. Prove that MT.TN + PT.TQ + PT.TL ≤ R², where R is the radius of the circumference prescribed around the ▲ABC.
Problem of the Week

The Latest Topics From the Math Forum

2^n = k(mod 7)(Rock'n'roller)
If (x = 0, 1, 2) and prove that

first derivativ(missayhl)
what's the first derivative for: x2(x+1)3

Equation with two variables(MM)
Prove that the equation has no natural solutions.

7th grade third round Bulgaria 2007(MM)
In my opinion that's a very good geometrical porblem. Let M an N be the midpoints of the cathetuses AC and BC in right-angled triangle ABC. A line through M parallel to AB intersects the angle bisecto

Circles, points(MM)
Let m be the number of the overall points of n circles. Let all their overall points are finite number. Find the maximal value of m.

The Latest Posts From the Math Forum

first derivativ(Fed_BG) ...

Solve the irrational equation(Rock'n'roller) Let x = a2 - 1 We have Then we solve the system m + 2p = -7 n + mp + 2q = -1 np + mq = 7 nq = 2 And then it's easy :) ...

Equation with two variables(MM) So there is a problem with the first equation. Fed_BG noticed it. So prove that there are no solutions for ...

A logical problem with numbers(Fed_BG) Try this one: 1 4 5 9 10 15 ...

A logical problem with numbers(Fed_BG) Nice problem. Let's assume the sequence that way: 13122833143053163... Now divide the sequence into triplets: 131 228 331 430 531 63... Notice all the triplets start with consecutively natural nu ...