1,122
edits
Changes
From Karnataka Open Educational Resources
no edit summary
The circle is the most primitive and rudimentary of all human inventions, and at the same time, the most dynamic. It is the cornerstone in the foundation of science and technology. It is the basic tool of all engineers and designers. It is used by the greatest artists and architects in the history of mankind. Without a circular shape the wheel, pulleys, gears, ball bearings and a thousand other items we take for granted wouldn’t exist. And of course we would never have the pleasure of driving a car, riding a giant wheel, or watching the moon landing on our television set.<br>
The circle is the most primitive and rudimentary of all human inventions, and at the same time, the most dynamic. It is the cornerstone in the foundation of science and technology. It is the basic tool of all engineers and designers. It is used by the greatest artists and architects in the history of mankind. Without a circular shape the wheel, pulleys, gears, ball bearings and a thousand other items we take for granted wouldn’t exist. And of course we would never have the pleasure of driving a car, riding a giant wheel, or watching the moon landing on our television set.<br>
If you look through any old patent claim, you will most likely find the repeated use of circles, spheres, curves, arches, etc. circles are everything and they are nothing. They don’t exist in reality and yet they are the basis of all that mankind has brought into existence. That is why a circle is so fantastic.
If you look through any old patent claim, you will most likely find the repeated use of circles, spheres, curves, arches, etc. circles are everything and they are nothing. They don’t exist in reality and yet they are the basis of all that mankind has brought into existence. That is why a circle is so fantastic.
=== Circle Properties ===
* A circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane.
* Equal chords of a circle (or of congruent circles)subtend equal angles at the centre.
* If the angles subtended by two chords of a circle(or of congruent circles) at the centre(corresponding centres) are equal, the chords are equal.
* The perpendicular from the centre of a circle to a chord bisects the chord.
* The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.
* There is one and only one circle passing through three non-collinear points.
* Equal chords of a circle (or of congruent circles) are equidistant from the centre (or corresponding centres).
* Chords equidistant from the centre (or corresponding centres) of a circle (or of congruent circles) are equal.
* If two arcs of a circle are congruent, then their corresponding chords are equal and conversely if two chords of a circle are equal, then their corresponding arcs (minor, major) are congruent.
* Congruent arcs of a circle subtend equal angles at the centre.
* The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
* Angles in the same segment of a circle are equal.
* Angle in a semicircle is a right angle.
* If a line segment joining two points subtends equal angles at two other points lying on the same side of the line containing the line segment, the four points lie on a circle.
* The sum of either pair of opposite angles of a cyclic quadrilateral is 1800.
* If sum of a pair of opposite angles of a quadrilateral is 1800, the quadrilateral is cyclic.
===Activities===
===Activities===
