GEOMETRY Circle Terminology

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

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

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

Diameter d=2r 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 Radius d=2r

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Tangents of the circle

Requirements:- Compass Pencils Eraser Scale Set Square

Tangent Chord Secent 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

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

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

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

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

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

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

When two concurrent circles We can not construct any common tangent

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

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

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