Center of a circle A fixed point inside a circle that is the same - PowerPoint PPT Presentation

D AY 2 – D EFINITION OF CIRCLES AND LINE SEGMENTS

I NTRODUCTION We encounter circular objects in real life such as: pizzas, wheels, tires, rings, cakes, coins, buttons, clocks and rims. On the other hand, line segments abound in real life. The edge of a book and the vertical corner of a wall form line segments. We are going to define circles and identify various parts of a circle.

V OCABULARY Circle A two dimensional shape made up points, all having the same distance from a given point called the center of the circle. Subtended angle The angle formed by an arc or a line at a given point. Line segment A portion of a line between two endpoints. Line segment AB, written as 𝐵𝐶 is shown below. B A

Center of a circle A fixed point inside a circle that is the same distance from every point on the circle. Circles are named basing on their center. In circle O, the center is shown. Center O

Example 1 Draw and label GH . Solution GH is a line segment by definition. G H

Example 2 From the figure below, list all the line segments. A B E D C F

Solution 𝐸𝐹, 𝐸𝐶, 𝐶𝐹, 𝐺𝐶, 𝐵𝐶, 𝐶𝐷, 𝐵𝐷

P ARTS OF A CIRCLE  Radius The distance from the center of a circle to any point on the circle. Radius O

Chord A straight line that joins any two points on the circle, or simply a line segment whose endpoints lie on the circle. PQ and RS are chords. Q P R S

Diameter A line segment which goes through the center of the circle and whose both endpoints lie on the circle, or simply a chord which passes through the center of the circle. The diameter is the longest chord in a circle. 𝐵𝐶 is the diameter. B A O

Circumference The distance around the edge of a circle, or simply the perimeter of a circle. Arc Part of the circumference of a circle. An arc is named according to its endpoints. AB is an arc. Minor arc Major arc

Semi circle A half circle formed when we cut a circle along its diameter. Minor arc An arc whose length is less than the length of the arc of the semicircle. Major arc An arc whose length is more than the length of the arc of the semi circle.

In the figure below, AB is the minor arc and ACB is the major arc . Minor arc Major arc

Segment The region of a circle bounded by a chord and an arc. A chord divides a circle into two parts called segments. (a) Major segment Region bounded by the chord and the major arc. (b) Minor segment Region bounded by the chord and minor arc.

Major and minor segments are shown below. Major segment Minor segment

Central angle An angle whose vertex is the center of a circle. Central angle

Sector The region of a circle enclosed by two radii and an arc. Radius A Minor sector B O Major sector

Secant A straight line that intersects a circle twice. Secant

Tangent to a circle A straight line in the plane of a circle that touches the circle at only one point without crossing it. The point at which the tangent touches the circle is called the point of tangency . Tangent line Point of tangency

Concentric circles Two or more circles with different radii but having a common center. The diagram below shows two concentric circles. Congruent circles These are equal circles because they have the equal radii.

Eccentric circles Two or more circles are said to be eccentric if they have different centers though located within one or more of the circles. D C

Example 3 Identify whether the lines or line segments are chords, secants, tangents, diameters or radii of the circle below. (a) 𝑄𝑅 F (b) 𝑈𝑉 A D (c) 𝑋𝑌 E O (d) 𝑆𝑇 H (e) 𝑃𝑅 B C G

Solution (a) 𝐵𝐶 is a diameter. (b) 𝐷𝐸 is a chord. (c) 𝐻𝐼 is a tangent. (d) 𝐹𝐺 is a secant. (e) 𝑃𝐶 is the radius.

Example 4 The diameter of circle is given as 7.4 in. Find the radius. Solution The diameter of a circle is twice its radius, 7.4 therefore, the radius is 2 = 3.5 𝑗𝑜. Example 5 If the radius of a circle is 15.4 ft . what is its diameter? Solution Diameter = 2 × 𝑠𝑏𝑒𝑗𝑣𝑡 = 2 × 15.4 = 30.8 𝑔𝑢

H OMEWORK Identify whether the lines or line segments are chords, secants, tangents, diameters or radii of the circle below. (a) 𝐵𝐸 E (b) 𝐵𝐶 A B (c) 𝐹𝐺 (d) 𝐻𝐼 C (e) 𝐷𝐸 H (f) 𝐵𝐷 D G F

A NSWERS TO HOMEWORK (a) 𝐵𝐸 is the diameter (b) 𝐵𝐶 is a chord (c) 𝐹𝐺 is a tangent (d) 𝐻𝐼 is a secant (e) 𝐷𝐸 is a radius (f) 𝐵𝐷 is a radius

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