## Basic and Rich Geometry Concepts part 4, Proof of arc angle subtending concept

Arcs and subtended angles: Any arc in a circle will subtend an angle at the centre twice the angle it subtends at any point on its complementary arc.

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Basic concepts on a subject form the foundation. Tutorials are for building the foundational concepts in concise but comprehensive manner.

In work life and personal life often we need to learn the basics on a subject quickly. Usually it is not easy to acquire the basic concepts on any subject reliably in a short time from a concise material.

Basic concepts on any subject form the foundation, but generally we have found it is not easy to build it in a short time. Our focus here is on **base concepts** in a concise form that can be learned quickly and be used as a launch pad for further learning and subject specific problem solving.

Often we added a **rich concept layer** derived from the base concepts that helps to solve more complex problems with great ease. For us, it is a two layer concept model: Base concepts and Rich concepts derived from base concepts. Objective is efficient problem solving.

* Basic maths:* Basic concepts on maths. The content is primarily targeted for competitive test requirements.

* Reasoning and logic analysis:* Tutorials, problems and puzzles on competitive test reasoning and logic analysis.

Submitted by Atanu Chaudhuri on Wed, 17/08/2016 - 07:15

Arcs and subtended angles: Any arc in a circle will subtend an angle at the centre twice the angle it subtends at any point on its complementary arc.

Submitted by Atanu Chaudhuri on Tue, 12/07/2016 - 11:03

Traveling at same speed we would need twice the time we took last time, if we have to cover twice the distance we traveled last time. This follows from our common sense. The relationship between speed, time and distance is one of the most basic physical laws that affects our real life experiences extensively. Trains run from station to station at various speeds; boats ply in the river but their actual speeds are reduced by the river stream speed if the boat moves upstream...the applications of the relationship between speed time and distance form an important part of Arithmetic...

Submitted by Atanu Chaudhuri on Thu, 30/06/2016 - 09:47

Different persons or types of persons complete the same work in different number of days as their work capacities are different. For example, a boy may complete a work in 6 days while a man may complete the same work in 3 days. In work-wage problems these work rates become important as the working agents receive wages in ratio of their work capacities. Finally, in pipes and cisterns problems similar working agents come into action in the form of pipes but they receive no wages...

Submitted by Atanu Chaudhuri on Wed, 08/06/2016 - 17:13

When two materials are mixed together in a certain ratio homogeneously, a mixture is formed. Various operations on such a mixture give rise to the topic of Mixture. Usually liquids that can be mixed are used in mixtures. Examples are, Water and milk, Water and fruit juice. Alloys are also formed by mixing metals through specific processes. Grains of same cereal of different price can be mixed giving rise to a grain mixture of another price...

Submitted by Atanu Chaudhuri on Mon, 30/05/2016 - 20:49

A ratio defines how many times is one quantity with respect to another of same type. It is expressed as a minimized fraction and its numerator is called antecedent and denominator consequent. In practice these terms are not very important...

Submitted by Atanu Chaudhuri on Fri, 27/05/2016 - 21:09

Trigonometry concepts: Trigonometry functions, function values, identities, compound angle, multiple angle functions, laws of sine and applications.

Submitted by Atanu Chaudhuri on Tue, 24/05/2016 - 12:08

Circle basic concepts: Chords, arcs, tangents, cyclic quadrilateral, angle subtended by a chord and secant of a circle with examples and exercise.

Submitted by Atanu Chaudhuri on Sun, 22/05/2016 - 23:03

Quadrilateral basic Concepts: Properties of a quadrilateral, polygons, squares, parallelograms, rhombus, cyclic quadrilateral with examples and exercise.

Submitted by Atanu Chaudhuri on Fri, 20/05/2016 - 19:46

Geometry basics points lines and triangles: Straight lines, parallel lines, angles, triangles, properties of triangles with examples and exercise.

Submitted by Atanu Chaudhuri on Wed, 18/05/2016 - 14:58

Fractions decimals basic concepts, arithmetic operations on fractions, conversion of fraction to decimal, rational irrational numbers, surds and more.