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Math Lesson- Circles

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GMAT Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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Math Lesson- Circles [#permalink]  02 Oct 2016, 09:25
Expert's post

Math Lesson- Circles

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.

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.

• 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.

Basic properties of a circle

• Angle in a semicircle is the right angle.
• Angle in the same segment of a circle are equal.

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Sandy
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Re: Math Lesson- Circles [#permalink]  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.
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

Re: Math Lesson- Circles [#permalink]  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]  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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