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Circle theorems are fundamental rules in geometry that explain relationships between angles, lines, and arcs in circles. They include theorems on right angles subtended by diameters, the relationship between central and circumferential angles, equality of angles from the same chord, properties of cyclic quadrilaterals, the alternate segment theorem, tangents from a point, and bisecting chords with a perpendicular radius. These theorems are vital for calculating unknown angles and solving geometric problems.
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Circle theorems are a set of rules in geometry that explain the relationships between angles, lines, and arcs within and around a circle
Circle theorems are crucial for solving complex geometric problems and are a standard part of mathematical education
Circle theorems have significant practical applications in geometry, such as calculating unknown angles and determining measures of unknown angles in figures
The angle subtended by a diameter at the circumference of a circle is a right angle
The central angle is twice the size of the circumferential angle when subtending the same arc
Angles subtended by the same chord in the same segment of a circle are equal
The sum of the opposite angles in a cyclic quadrilateral is 180°
The angle between a tangent to a circle and a chord drawn from the point of tangency is equal to the angle in the alternate segment of the circle
Tangents from a single point outside a circle are equal in length
A radius perpendicular to a chord bisects the chord
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Definition of Circle Theorems
Rules explaining relationships between angles, lines, arcs in/on a circle.
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Importance of Circle Theorems
Essential for solving complex geometric problems, integral in math education.
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Example of a Circle Theorem
Angle at circumference subtended by diameter is always 90°.
