Q1 of 15 Page 87

In a circle, a chord 1 centimetre away from the centre is 6 centimetres long. What is the length of a chord 2 centimetres away from the centre?


O is centre of the circle.


DE is the chord 1 cm away from centre. CH is perpendicular on DE.


∴ CH = 1 cm and DE = 6 cm


FG is the chord 2 cm away from centre. CI is perpendicular on FG.


∴ CI = 2 cm


From centre C, CE and CG are joined.


CE and CG both are radius of the circle.


In ΔCHE we have,


∠CHE = 90° [∵CH is perpendicular on DE]


CH = 1 cm


HE = DE/2 = 3 cm [∵perpendicular drawn from centre bisects chord]



In ΔCGI we have,


∠CIG = 90° [∵CI is perpendicular on FG]


CI = 2 cm


CG = CE = √10 cm



∴ FG = 2 × IG = 2√6 cm [∵perpendicular drawn from centre bisects chord]


∴ The length of the chord is = 2√6 cm


More from this chapter

All 15 →
2

Two chords intersect at a point on a circle and the diameter through this point bisects the angle between the chords. Prove that the chords have the same length.

 3

In the picture on the right, the angles between the radii and the chords are equal.


Prove that the chords are of the same length.

 2

In a circle of radius 5 centimetres, two parallel chords of lengths 6 and 8 centimetres are drawn on either side of a diameter. What is the distance between them? If parallel chords of these lengths are drawn on the same side of a diameter, what would be the distance between them?

 3

The bottom side of the quadrilateral in the picture is a diameter of the circle and the top side is a chord parallel to it. Calculate the area of the quadrilateral.