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Math Lesson- Circles

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CEO
CEO
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Joined: 07 Jun 2014
Posts: 2841
GRE 1: 323 Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 789 [0], given: 134

Math Lesson- Circles [#permalink] New post 02 Oct 2016, 09:25
Expert's post

Math Lesson- Circles



Image

Radius: A line segment drawn joining the centre and the boundary line (known as circumference) is called the Radius of the circle.
Diameter: A line segment crossing the circle passing through the centre of the circle.
Circumference: The boundary or the perimeter of the circle.
Chord: A line segment joining any two points on the circumference of the circle.
Arc: Part of the circumference of the circle.
Tangent: A line that touches the circumference of the circle at exactly one point.
Sector: An area enclosed by two radii of a circle.

Basic formulae of a circle:
circumference = 2*pi*r, where r is the radius of the circle.
area = pi*r^2
diameter = 2*r

Properties of Arcs and angles :
The angle made by the ends of the arc at the centre of the circle is called its angle.

  • Equal arcs subtend equal angles at the centre of the circle and vice versa.
  • The angle at the centre od the circle is twice the angle at the circumference subtended by the same arc.


Image



Properties of Chords and tangents:


  • Diameter is the longest chord of a circle.
  • A perpendicular line from the centre to the chord bisects the chord.
  • Equal chords are equidistant from the centre of the circle.
  • Equal chords subtend equal angles at the centre of the circle.

Image

  • A tangent to a circle is perpendicular to the radius drawn at the point of contact.
  • Tangents to a circle from an exterior point are equal.
  • The angle between the tangent and the chord is equal to the inscribed angle on the opposite side of the chord.


Image

Basic properties of a circle

  • Angle in a semicircle is the right angle.
  • Angle in the same segment of a circle are equal.
Image
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Sandy
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Joined: 16 Dec 2016
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Re: Math Lesson- Circles [#permalink] New post 20 Jun 2017, 03:24
Hey I'm not clear with the following two points can you please elaborate them a bit-
1] The angle between the tangent and the chord is equal to the inscribed angle on the opposite side of the chord.
2] Angle in the same segment of a circle are equal.
CEO
CEO
User avatar
Joined: 07 Jun 2014
Posts: 2841
GRE 1: 323 Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 46

Kudos [?]: 789 [0], given: 134

Re: Math Lesson- Circles [#permalink] New post 20 Jun 2017, 06:30
Expert's post
1] The angle between the tangent and the chord is equal to the inscribed angle on the opposite side of the chord.

Here is a detailed proof: https://brilliant.org/wiki/alternate-segment-theorem-2/

2] Angle in the same segment of a circle are equal.[/quote]
Here is the problem definition: http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/circles2hirev4.shtml

Here is the proof: https://proofwiki.org/wiki/Angles_in_Same_Segment_of_Circle_are_Equal
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Re: Math Lesson- Circles [#permalink] New post 20 Jun 2017, 08:27
sandy wrote:
1] The angle between the tangent and the chord is equal to the inscribed angle on the opposite side of the chord.

Here is a detailed proof: https://brilliant.org/wiki/alternate-segment-theorem-2/

2] Angle in the same segment of a circle are equal.

Here is the problem definition: http://www.bbc.co.uk/schools/gcsebitesize/maths/geometry/circles2hirev4.shtml

Here is the proof: https://proofwiki.org/wiki/Angles_in_Same_Segment_of_Circle_are_Equal[/quote]


Got that. That was really helping, infact got cleared with some more concepts. tysm!
Re: Math Lesson- Circles   [#permalink] 20 Jun 2017, 08:27
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Math Lesson- Circles

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