Chapter 9 CIRCLES here are the definitions and key concept explanations
Fundamental Definitions
- Circle A circle is the collection of all points in a plane, which are equidistant from a fixed point in the plane.
Definitions Related to Angles and Segments
- Angle Subtended by a Line Segment Take a line segment PQ and a point R not on the line containing PQ. Join PR and QR. Then ∠ PRQ is called the angle subtended by the line segment PQ at the point R.
- Examples: ∠ POQ is the angle subtended by the chord PQ at the centre O. ∠ PRQ and ∠ PSQ are respectively the angles subtended by PQ at points R and S on the major and minor arcs PQ.
- Angle Subtended by an Arc at the Centre The angle subtended by an arc at the centre is defined to be angle subtended by the corresponding chord at the centre.
- The minor arc subtends the angle (e.g., ∠POQ in Fig 9.14), and the major arc subtends the reflex angle (e.g., reflex angle POQ in Fig 9.14).
- Angle Formed in the Segment If points P and Q are joined to form a chord PQ (where A is any point on the remaining part of the circle), then ∠ PAQ is also called the angle formed in the segment PAQP.
Definitions Related to Distance
- Distance of a Line from a Point The length of the perpendicular from a point to a line is defined as the distance of the line from the point.
- Note: If the point lies on the line, the distance of the line from the point is zero.
Definitions Related to Quadrilaterals
- Cyclic Quadrilateral A quadrilateral ABCD is called cyclic if all the four vertices of it lie on a circle.
Abbreviation
- CPCT This is the abbreviation used for ‘Corresponding parts of congruent triangles’.