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GEOMETRYGEOMETRY Circle Terminology

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Component of Geometry Point (dot) Line At least two points given Angle If two line intersect in a point Plane Something which has area Space something which boundary at least by two plane

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Circle Set of points which have same distance into one permanent point Same distance = radius = r Permanent point is central point

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Radius (or Radii for plural) The segment joining the center of a circle to a point on the circle. Example: OA adopted from http://www.worldofteaching.com http://www.worldofteaching.com

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Diameter A chord that passes through the center of a circle. Example: AB What is AO? What is OB? What is relation between radius and diameter? Radius d=2r

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Chord A segment joining two points on a circle Example: AB

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Chord A segment joining two points on a circle Example: AB AB= diameter So, what is relation between chord and diameter? Diameter is the longest chord

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Secant A line that intersects the circle at exactly two points. Example: AB

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Secant A line that intersects the circle at exactly two points. Example: AB

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Tangent A line that intersects a circle at exactly one point. Example: AB

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Central Angle An angle whose vertex is at the center of a circle. Example: Angle ABC

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Inscribed Angle An angle whose vertex is on a circle and whose sides are determined by two chords. Example: Angle ABC

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Arc A figure consisting of two points on a circle and all the points on the circle needed to connect them by a single path. Example: arc AB What is the longest arc?circumference

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Intercepted Arc An arc that lies in the interior of an inscribed angle. Example: arc AC

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Two Intercepted Arc If angle is inside the circle. Example: arc AC arc DF

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If angle is outside the circle. Example: arc DE arc DC Two Intercepted Arc

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Apothem The shortest distance between center point and chord Example: OA A

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Segment Area which bordered by arc and chord Shaded area is minor segment Plain area is major segment O

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Sector Area which bordered by two radii and an arc Shaded area is minor sector Plain area is major sector O

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Requirements:- Compass Pencils Eraser Scale Set Square

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If line touches the circle at one point only that is called a tangent If line connect the two point at the circle that is called a chord If line intersect the circle at two point that is called secant

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Formation of tangent Circle A B Secant C D Chord P Tangent

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APB is called a tangent to the circle The touching point P is called the point of contact. C A B P

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A B C D E F G H P Q We construct four tangents AB,CD, EF & GH When two circles do not touch

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A B C D O O’O’.. We can construct three tangents APB, CQD, PRQ When two circles touches externally P Q 1 st Tangent 2 nd Tangent 3 rd Tangent R

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When two circles intersect each other AB C D 1 st Tangent 2 nd Tangent O O !.. We can construct two tangents AB, CD

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A B OO’ When two circles touches internally We can construct only one tangents APB P

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When two concurrent circles O O’ We can not construct any common tangent

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P P is a point out side the circle you can construct two tangents passing through P O Q R Tangent PQ = TangentPR

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A B C o Constructing Circumcircle Steps of Construction Construct a Δ ABC Bisect the side AB Bisect the side BC The two lines meet at O From O Join B Taking OB as radius draw a circumcircle.

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A B C Constructing of incircle Steps of construction Construct a Δ ABC The two lines meet at O Taking OP as radius Draw a circumcircle Bisect the ABC Bisect the BAC Taking O draw OP AB O P

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