"How do I involve my child in challenging mathematics? He gets good marks in school tests but I think he is smarter than school curriculum." "My daughter is in 4th grade. What competitions in mathematics and science can she participate in? How do I help her to perform well in those competitions?" "I have a […]
What is RMO? RMO or Regional Math Olympiad is the second round of Mathematics Contest in India after the Pre-regional Mathematics Olympiad (Pre-RMO or PRMO) leading to the prestigious International Mathematics Olympiad (IMO). It is held in the month of December (the first Sunday of December). The test is conducted in each of the 19 […]
Problem: Let ABCDE be a regular pentagon inscribed in a circle. P be any point in the minor arc AE. Prove that PA + PC + PE = PB + PD Proof: Suppose length of each side is 's' and each diagonal is 'x'. Apply Ptolemy's Theorem in PABC. We have PA . s + […]
In this post, here are problems from Regional Mathematics Olympiad, RMO 2011 Re-Test Paper. Let ABC be an acute angled scalene triangle with circumcenter O and orthocenter H. If M is the midpoint of BC, then show that AO and HM intersect at the circumcircle of ABC. Let n be a positive integer such […]
Let $ABC$ be a triangle. Let $D, E, F$ be points respectively on the segments $BC, CA, AB$ such that $AD, BE, CF$ concur at the point $K$. Suppose $\frac{BD}{DC} = \frac{BF}{FA}$ and $∠ADB = ∠AFC$. Prove that $∠ ABE = ∠ CAD$. Let $ (a_1a_2a_3.....a_{2011}) $ be a permutation (that is arrangement) of the […]
In this post, there are problems from Regional Mathematics Olympiad, RMO 2010. Try out these problems. Let $ABCDEF$ be a convex hexagon in which the diagonals $AD, BE, CF$ are concurrent at $O$. Suppose the area of triangle $OAF$ is the geometric mean of those of $OAB$ and $OEF$; and the area of the triangle […]
In this post, there are problems from Regional Mathematics Olympiad, RMO 2009. Try out these problems. Let $ABC$ be a triangle in which $AB = AC$ and let $I$ be its in-centre. Suppose $BC = AB + AI$. Find $∠BAC$.Discussion Show that there is no integer a such that $ a^2-3a-19 $ is divisible by […]
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 […]