Circle Geometry

studycat
Mind Map by , created over 6 years ago

Higher School Certificate(HSC ) MATHEMATICS Mind Map on Circle Geometry, created by studycat on 06/28/2013.

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studycat
Created by studycat over 6 years ago
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Circle Geometry
1 OTHER
1.1 When two circles touch, their centres and the point of contact are collinear
1.2 The products of the intercepts of two intersecting chords are equal
2 CHORDS
2.1 Chords of equal length subtend equal angles at the centre of the circle
2.2 Equal chords are equidistant from the centre of the circle
2.3 The perpendicular from the centre of a circle to a chord bisects the chord
2.3.1 The perpendicular bisector of a chord passes through the centre of the circle
3 ANGLES
3.1 Angles in the same segment are equal
3.2 The angle at the centre is twice the angle at the circumference subtended by the same arc
3.3 The angle in a semi-circle is a right angle
3.4 Opposite angles of a cyclic quadrilateral are supplementary
4 SECANTS & TANGENTS
4.1 The angle between a tangent and radius at the point of contact is 90 degrees
4.2 The tangents to a circle from an external point are equal in length
4.3 The angle between a tangent and a chord at the point of contact is equal to the angle in the alternate segment
4.4 The angle between the tangent and radius at the point of contact is a right angle
4.5 The product of the intercept of two intersecting secants to a circle from an external point are equal
4.6 The square of the tangent to a circle from an external point equals the product of the intercepts of any secant from the point

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