At Ramsetu
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Summary of “CIRCLES.”
Explanation of key concepts and properties.
Detailed examples and exercises.
Practical applications and relevance of circles in everyday life.
Key Concepts and Definitions:
Circle: A set of all points in a plane that are at a fixed distance from a fixed point called the center.Radius: A line segment from the center to any point on the circle.Diameter: A line segment passing through the center of the circle with both endpoints on the circle.Chord: A line segment with both endpoints on the circle.Secant: A line that intersects a circle in two points.Tangent: A line that touches the circle at exactly one point.
Chapter Content:
Summary of “CIRCLES”:
Introduction to circles and their basic properties.
Understanding different parts of a circle.
Important theorems related to circles.
Key Concepts:
Parts of a Circle:
Radius, diameter, chord, secant, tangent, arc, sector, segment.
Important Theorems:
Theorem 1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.Theorem 2: The lengths of tangents drawn from an external point to a circle are equal.Theorem 3: The angle subtended by an arc at the center is twice the angle subtended by it at any point on the remaining part of the circle.Theorem 4: The angle in a semicircle is a right angle.Theorem 5: Opposite angles of a cyclic quadrilateral are supplementary.
Formulas and Properties:
Circumference of a Circle: C=2πrC = 2\pi rC=2πrArea of a Circle: A=πr2A = \pi r^2A=πr2Length of an Arc: Length=θ360∘×2πr\text{Length} = \frac{\theta}{360^\circ} \times 2\pi rLength=360∘θ×2πrArea of a Sector: Area=θ360∘×πr2\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2Area=360∘θ×πr2
Applications:
Real-life applications of circles in design, engineering, architecture, and nature.
Solving problems involving angles, lengths, and areas related to circles.
Frequently Asked Questions (FAQs): 