The Problem! Let ABC be a triangle in which AB = AC and let I be its in-centre. Suppose BC = AB + AI. Find ∠BAC. VideoBig Ideas For any triangle ABC, \( \frac{\sin A}{a} = \frac{\sin B } {b} = \frac {\sin C }{c} \). Addendo: If \( \frac{a}{b} = \frac{c}{d} \) then...

Recently, French mathematician Cedric Villani’s team came up with ’21 measures for the teaching of Mathematics’. I read through the report, with great curiosity and happily noted that Cheenta’s Thousand Flowers program has already implemented...

The Problem Find the number of integer-sided isosceles obtuse-angled triangles with perimeter 2008. Video LectureKey ideas Cosine Rule: If ABC is any triangle, \( \angle BAC = \theta \) then \( AB^2 + AC^2 – 2\times AB \times AC \times \cos \theta = BC^2 \) ....

Problem 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 circum-radius of ABC. VIdeo DiscussionTheorems and tools The...

In a quadrilateral ABCD. It is given that AB=AD=13 BC=CD=20,BD=24. If r is the radius of the circle inscribable in the quadrilateral, then what is the integer close to r? Hint 1 - Draw a PictureHint 2 - Find out ACHint 3 - inradius and area is related Drawing a good...

Let \( \{a_n\}_{n\ge 1} \) be a sequence of real numbers such that $$ a_n = \frac{1 + 2 + … + (2n-1)}{n!} , n \ge 1 $$ . Then \( \sum_{n \ge 1 } a_n \) converges to ____________ Hint 1 - Sum of oddsHint 2 - Break in partialsHint 3 - Something goes to e! Notice...