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Circles

45 Videos

02:16 Hours

"Try solving this riddle. I have no vertices. I have no flat faces. I have infinite axes of symmetry. Who am I? It’s a Circle. We find circular objects everywhere from round cakes and bangles, to dartboard and cycle wheels. No wonder, the world of circles takes us to another tangent. Surprisingly, tangents are exclusively related to circles. Want to know how? Let us find that out in this chapter!"

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This course is offered in the following plan(s)

Math

Course Content

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Basics - Part 1 3 Topics Preview

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What is a Circle?

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How do we Define a Circle?

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What are the Different Regions Associated with a Circle?

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Basics - Part 2 4 Topics

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What is the Circumference?

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What is the Area of a Circle? Part 1

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What is the Area of a Circle? Part 2

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Chords 2 Topics

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What is a Chord?

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What is the Distance of a Chord from the Centre? What does a Chord Divide a Circle into?

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What are Arcs? How do we name them?

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What is the Degree Measure of an Arc?

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What is the Length of an Arc?

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Segments 3 Topics

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What are Segments? What are their Types?

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What is the Angle of a Segment?

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What is the Measure of the Angle formed in a Semi-Circle?

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Sectors 3 Topics

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What are Sectors? What are their Types?

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What is the Area of a Sector?

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What are Quadrants and Semi Circles?

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Circle, Lines and Points on Plane 5 Topics

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What are Concentric Circles?

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What are Congruent Circles?

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In how many ways can Circle and Lines lie on a Plane?

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How many Circles can pass through One point; Two points; or Three points?

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How do we prove that only one Circle can pass through Three Non-Collinear Points?

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Perpendicular to the Chord 2 Topics

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How do we Prove that the Perpendicular from the Centre of the Circle to the Chord Bisects the Chord?

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How do we Prove that the Line joining the Centre of the Circle and the Midpoint of the Chord is Perpendicular to that Chord?

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Equal Chords 2 Topics

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How do we Prove that Equal Chords are Equidistant from the Centre?

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How do we Prove that the Chords which are Equidistant from the Centre are Equal?

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Unequal Chords 2 Topics

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How do we Prove that Chords which are Bigger in Length are Closer to the Centre?

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How do we Prove that the Chord Closer to the Centre is Bigger in Length?

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Angles Subtended by Chords at the Centre 2 Topics

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How do we Prove that Congruent Chords of a Circle Subtend Congruent Angles at the Centre?

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How do we Prove that Chords subtending Equal Angles at the Centre are Equal?

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Angle formed by an Arc at the Centre 2 Topics

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How is the Angle formed by an Arc at the Centre related to the Angle formed by the Arc in the remaining part of the Circle?

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Can we prove that the Angle formed by an Arc at the Centre is Twice that formed by the Arc in the remaining part of the Circle?

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Angles formed in a Segment 4 Topics

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Are the Angles formed in the Same Segment Equal?

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How do we Prove that the Angles formed in the Same Segment are Equal?

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How do we Prove that the Angle in a Semicircle is a Right Angle?

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How do we Prove that the Arc of a Circle Subtending a Right Angle in its Alternate Segment is Semi Circular?

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Concyclic Points 2 Topics

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What are Concyclic Points?

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Concyclic Points - Proof

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Cyclic Quadrilaterals 4 Topics

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What is the Sum of the Measure of Opposite Angles in a Cyclic Quadrilateral?

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How do we Prove that the Opposite Angles of a Cyclic Quadrilateral add up to 180 degrees?

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What is the Quadrilateral which has its Opposite Angles add up to 180 degrees called?

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How do we Prove that if the Sum of Opposite Angles of a Quadrilateral is 180 degrees, then it is Cyclic?

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Cyclic Quadrilaterals - Exterior Angle 2 Topics

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How is the Exterior Angle of a Cyclic Quadrilateral related to its Interior Angles?

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How do we Prove that the Exterior Angle of a Cyclic Quadrilateral is Equal to its Interior Opposite Angle?

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Speed of a Sound Wave and Wave Equation

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Math

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