Revision Notes: Circle: Arc and Cyclic Properties | Mathematics Class 10 ICSE PDF Download

Some terms associated with circle

• Circles having the same centre but with different radii are said to be concentric circles.
• Two circles are said to be equal or congruent if they have equal radii.
• A circle passing through all the vertices of a polygon is called circumscribed circle of the polygon and its centre is called circumcentre.
  The polygon is called inscribed polygon.
• A circle touching all the sides of a polygon is called an inscribed circle of the polygon and its centre is called incentre.
• The line segment joining any two points on the circumference of the circle is called a chord of the circle.
• A chord of a circle passing through its centre is called a diameter of the circle
• A straight line drawn from the centre of a circle to bisect a chord which is not a diameter is at right angles to chord.
• Perpendicular drawn to a chord from the centre of a circle bisects the chord.
• One and only one circle passes through three given points not in a straight line.
• Equal chords are equidistant from centre.
• Chords which are equidistant from the centre are equal in lengths.

Arc

The whole arc of a circle is called the circumference of the circle.

One-half of the whole arc of a circle is called a semi-circle of the circle.

Segment of a Circle

Relation between Arcs and Segments

Cyclic Properties

The opposite angles of a cyclic quadrilateral are supplementary.
If a pair of opposite angles of a quadrilateral are supplementary, then the quadrilateral is cyclic.
The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle.