 Select Page

# What are we learning ?

Main idea: It is usually hard to solve biquadratic equations. However, sometimes, combining tools from geometry and strategies like completing the square it is possible to do so.

# Look at the knowledge graph. # Next understand the problem

Let a,b and c be the sides of a right angled triangle. Let $\displaystyle{\theta }$ be the smallest angle of this triangle. If $\displaystyle{ \frac{1}{a}, \frac{1}{b} }$ and $\displaystyle{ \frac{1}{c} }$ are also the sides of a right angled triangle then show that $\displaystyle{ \sin\theta=\frac{\sqrt{5}-1}{2}}$

##### Source of the problem

I.S.I. B.Stat. Entrance 2005, Subject Problem 1

6/10
##### Suggested Book
Challenges and Thrills in Pre College Mathematics

Excursion Of Mathematics

# Connected Program at Cheenta

#### I.S.I. & C.M.I. Entrance Program

Cheenta I.S.I., C.M.I. Entrance Program consists of live group and one on one classes, 24/7 doubt clearing and continuous problem solving streams. The trainers are / were students of Indian Statistical Institute and Chennai Mathematical Institute.

# Similar Problems ## Beautiful problems from Coordinate Geometry

The following problems are collected from a variety of Math Olympiads and mathematics contests like I.S.I. and C.M.I. Entrances. They can be solved using elementary coordinate geometry and a bit of ingenuity. ## An interesting biquadratic from ISI Entrance 2005

How to combine algebra and geometry to solve a biquadratic? Try this beautiful problem from ISI Entrance 2005. We provide knowledge graph and video. ## cos(sin(x)) function in ISI Entrance

A simple trigonometric equation from ISI Entrance. Try this problem. We also added a quiz, some related problems, and finally video. ## Geometry of AM GM Inequality

AM GM Inequality has a geometric interpretation. Watch the video discussion on it and try some hint problems to sharpen your skills. ## Counting triangles in ISI Entrance

Can you combine geometry and combinatorics? This ISI Entrance problems requires just that. We provide sequential hints, additional problems and video. ## Paper folding geometry in ISI Entrance

A problem from ISI Entrance that requires Paper folding geometry. We provide sequential hints so that you can try the problem!

## An Hour of Beautiful Proofs

Every week we dedicate an hour to Beautiful Mathematics - the Mathematics that shows us how Beautiful is our Intellect. This week, I decided to do three beautiful proofs in this one-hour session... Proof of Fermat's Little Theorem ( via Combinatorics )It uses... ## Inequality – In Equality

This article aims to give you a brief overview of Inequality, which can be served as an introduction to this beautiful sub-topic of Algebra. This article doesn't aim to give a list of formulas and methodologies stuffed in single baggage, rather it is specifically... ## AM GM inequality in ISI Entrance

Arithmetic Mean and Geometric Mean inequality form a foundational principle. This problem from I.S.I. Entrance is an application of that.

## How to solve an Olympiad Problem (Number Theory)?

Suppose you are given a Number Theory Olympiad Problem. You have no idea how to proceed. Totally stuck! What to do? This post will help you to atleast start with something. You have something to proceed. But as we share in our classes, how to proceed towards any...