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GEOMETRY 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

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**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

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

arc DC

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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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Tangents of the circle

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Requirements:- Compass Pencils Eraser Scale Set Square

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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

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

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**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

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**When two circles do not touch**

A B E H P Q G F C D We construct four tangents AB,CD, EF & GH

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**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

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**When two circles intersect each other**

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

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**When two circles touches internally**

P O O’ B We can construct only one tangents APB

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**When two concurrent circles**

We can not construct any common tangent

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**P is a point out side the circle you can construct two tangents passing through P**

Q P O R Tangent PQ = TangentPR

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**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

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**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

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