Circle: A circle is a collection of all points in a plane which are at a constant distance from a fixed point.
Centre: The fixed point is called the centre.
Radius: The constant distance from the centre is called the radius.
Chord: A line segment joining any two points on a circle is called a chord.
Diameter: A chord passing through the centre of the circle is called diameter. It is the longest chord.
Tangent: When a line meets the circle at one point or two coincidings The line is known as points, a tangent. The tangent to a circle is perpendicular to the radius through the point of contact. ⇒ OP ⊥ AB The lengths of the two tangents from an external point to a circle are equal. ⇒ AP = PB
Length of Tangent Segment PB and PA are normally called the lengths of tangents from outside point P.
Q1. Fill in the blanks:
(i) The centre of a circle lies in________of the circle.
(ii) A point, whose distance from the centre of a circle is greater than its radius lies in________of the circle.
(iii) The longest chord of a circle is a________of the circle.
(iv) An arc is a________when its ends are the ends of a diameter.
(v) Segment of a circle is the region between an arc and________ of the circle.
(vi) A circle divides the plane, on which it lies, in________parts.
Solution: (i) interior (ii) exterior (iii) diameter
(v) the chord (vi) three
Q2.Write True or False. Give reasons for your answers.
(i) Line segment joining the centre to any point on the circle is a radius of the circle.
(ii) A circle has only finite number of equal chords.
(iii) If a circle is divided into three equal arcs, each is a major arc.
(iv) A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
(v) Sector is the region between the chord and its corresponding arc.
(vi) A circle is a plane figure.
Class IX Math Circles (EXERCISE 10.1)
Solution:
(i) True [∵ All points on the circle are equidistant from the centre]
(ii) False [∵ A circle can have an infinite number of equal chords.]
(iii) False [∵ Each part will be less than a semicircle.]
(iv) True [∵ Diameter = 2 × Radius]
(v) False [∵ The region between the chord and its corresponding arc is a segment.]
