MathDB

6

Part of 2008 India Regional Mathematical Olympiad

Problems(2)

Number of triangles with integer sides and other conditions

Source: (Indian) RMO 2008 Problem 6

11/9/2008
Find the number of all integer-sided isosceles obtuse-angled triangles with perimeter 2008 2008. [16 points out of 100 for the 6 problems]
geometryperimeterinequalitiestrigonometrytriangle inequalitycombinatorics unsolvedcombinatorics
Trig bash

Source: Excursion

6/25/2020
Let BCDKBCDK be a convex quadrilateral such that BC=BKBC=BK and DC=DKDC=DK. AA and EE are points such that ABCDEABCDE is a convex pentagon such that AB=BCAB=BC and DE=DCDE=DC and KK lies in the interior of the pentagon ABCDEABCDE. If ∠ABC=120∘\angle ABC=120^{\circ} and ∠CDE=60∘\angle CDE=60^{\circ} and BD=2BD=2 then determine area of the pentagon ABCDEABCDE.
trigonometrygeometrypentagonconvex quadrilateral