Circle Vocabulary (वृत्त शब्दावली)

Circle Vocabulary

Circle: The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle. The fixed point is called the center of the circle and the fixed distance is called the radius of the circle.
Chord: If you take two points A and B on the circle, then the line segment joining AB is called the chord of the circle.
Diameter: A chord that passes through the center of the circle is called the diameter of the circle. Diameter is the longest chord of the circle and it is twice the length of the radius of the circle.
Arc: A piece of the circle between two points is called an arc.
Circumference: The length of the complete circle is called its circumference.
Segment: The region between a chord and either of its arc is called a segment.
Sector: The region between an arc and the radii joining the endpoints of the arc to the center of the circle is called a sector.

All the above are shown in the applet below, you may move the points on the two circles and see the effects.

वृत्त शब्दावली

वृत्त : एक तल पर उन सभी बिन्दुओं का समूह , जो तल के एक स्थिर बिन्दु से एक स्थिर दूरी पर स्थित हों , एक वृत्त कहलाता है। स्थिर बिन्दु को वृत्त का केन्द्र कहते हैं तथा स्थित दूरी को वृत्त की त्रिज्या कहते हैं।
जीवा : यदि एक वृत्त पर दो बिन्दु A और B लें , तो रेखाखण्ड AB वृत्त की जीवा कहलाता है।
व्यास : वह जीवा जो वृत्त के केन्द्र से होकर जाती है , उसे वृत्त का व्यास कहते हैं। व्यास , वृत्त की सबसे बड़ी जीवा होती है। व्यास की लंबाई वृत्त की त्रिज्या से दो गुनी होती है।
चाप : दो बिन्दुओं के बीच के वृत्त के भाग को चाप कहते हैं।
परिधि : संपूर्ण वृत्त की लंबाई को उस वृत्त की परिधि कहते हैं।
वृत्तखण्ड : जीवा और प्रत्येक चाप के मध्य क्षेत्र को वृत्तखण्ड कहते हैं।
त्रिज्यखण्ड : केन्द्र को एक चाप के सिरों से मिलाने वाली त्रिज्याओं एवं चाप के बीच के क्षेत्र को त्रिज्यखण्ड कहते हैं।

नीचे दी गयी एपलेट में उपर परिभाषित सभी अवधारणाओं को दर्शाया गया है , दोनों वृत्त में दिखाए गए बिन्दुओं को हिला कर आप उनका प्रभाव देख सकते हैं।

Polar Coordinates of a Point

Internal Common Tangents - Unequal Radius

Draw the given circles with centres O and P and radii R₁ and R₂ respectively such that 
R₁ > R₂

1. Draw a line joining the centres O and P.
2. With centre O and radius equal to (R₁ + R₂ ), draw a circle.
3. From P , draw a line PT tangent to this circle.
4. Draw a line OT cutting the circle at A.
5. Through P , draw a line PB parallel to OA , on the other side of OP and cutting the circle at B.
6. Draw a line through A and B. This is the required tangent.
7. Similarly , draw another internal tangent through C and D.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Common Tangents - Circles with Equal Radius

A. External Tangents
Draw the given circles with centres A and B

• Draw a line segment joining A and B
• At A and B construct perpendiculars to AB on its same side to intersect given circles at D and E.
• Draw a line joining D and E. This line is the required tangent. FG is the other tangent, which can be drawn similarly.

B. Internal Tangents
Draw the given circles with centres P and Q

• Draw a line segment joining P and Q.
• Bisect PQ at O. Draw a circle with OP as diameter to cut the circle at M and R.
• With centre O and radius OM , draw a circle to cut the other circle at S and N.
• Draw line through M and N. This is the required tangent.
• Similarly , draw a line through R and S , which is the other required tangent.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Properties of an Equilateral Triangle

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Sangaku-1

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

Circle Vocabulary

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)