Circle:Exercise - 10.1 (Mathematics NCERT Class 9th)


Q.1     Fill in the blanks :
(i)The center of a circle lies in ______ of the circle.(exterior/interior)
(ii) A point , whose distance from the center of a circle is greater than its radius lies in _______of the
circle (exterior/interior)
(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.

Sol.

(i) interior
(ii) exterior
(iii) diameter.
(iv) semi- circle
(v) chord
(vi) three parts.


Q.2     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.

Sol.

(i) True : As 'radius' is used in two sense - in the sense of a line segment and also in the sense of a length.
(ii) False : As an infinite number of points lie on the circle so we get infinite number of chord on joining any two points.
(iii) False : Since these arcs are equal in length so they are called equal arc.
(iv) True : As diameter is the longest chord and its length is twice the radius of the circle.
(v) False : As the region between an arc and the two radii, joining the center to end points of the are is known as a sector.
(vi) True : Since a circle is the locus of a point which moves in a plane in such a way that its distance from a given fixed point in the plane is always constant. So, a circle lies in a plane.



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