Let's discuss a problem based on Integer Sided Obtuse angled triangles with Perimeter. Find the number of integer-sided isosceles obtuse-angled triangles with perimeter 2008. (Indian RMO 2008) Discussion: Let the three sides be a, a and b. Hence 2a + b = 2008 ... (i) Using the triangular inequality we have 2a > b ...(ii) […]
In this post, there are problems from Regional Mathematics Olympiad, RMO 2008. Try out these problems. Let $ABC$ be an acute-angled triangle, let $D$, $F$ be the mid-points of $BC, AB$ respectively. Let the perpendicular from $F$ to $AC$ and the perpendicular at $B$ to $BC$ meet in $N$. Prove that $ND$ is equal to […]
A square sheet of paper ABCD is so folded that B falls on the mid-point of M of CD. Prove that the crease will divide BC in the ratio 5:3. Discussion: Assuming the side of the square is 's'. Let a part of the crease be 'x' (hence the remaining part is 's-x'). We apply […]
This post contains problems from Indian National Mathematics Olympiad, INMO 2012. Try them and share your solution in the comments. Problem 1 Let ABCD be a quadrilateral inscribed in a circle. Suppose AB =$latex \sqrt {2 + \sqrt {2} } $ and AB subtends 1350 at the center of the circle. Find the maximum possible […]
This post contains problem from Indian National Mathematics Olympiad, INMO 2011. Try them out and share your solution in the comments. Let D, E, F be points on the sides BC, CA, AB respectively of a triangle ABC such that BD = CE = AF and ∠BDF = ∠CED = ∠AFE. Prove that ABC […]
This a problem from from National Board for Higher Mathematics (NBHM) 2013 based on Cyclic Group Problem for M.Sc Students. Which of the following statements are true? Every group of order 11 is cyclic. Every group of order 111 is cyclic. Every group of order 1111 is cyclic. Discussion: Every group of order 11 is […]
View the other sections of this test. Algebra || Geometry Try a online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at helpdesk@cheenta.com View the other sections of this test. Algebra || Geometry Try a online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at […]
Section 3: Geometry View the other sections of this test. Algebra || Analysis Try an online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at helpdesk@cheenta.com Find the reflection of the point (2, 1) with respect to the line x=y in the xy-plane. Find the area of the circle in […]