Q5 of 100 Page 17

A chord of length 14 cm is at a distance of 6 cm from the centre of a circle. The length of another chord at a distance of 2 cm from the centre of the circle is

Let AB and CD be two chords of the circle.

Draw OM perpendicular to AB and ON = CD


AB = 14 cm


OM = 6 cm


ON = 2 cm


Let,


CD = x


In AOM,


AO2 = AM2 + OM2


= 72 + 62


AO2 = 85 (i)


In CON,


CO2 = ON2 + CN2


CO2 = 4 + (ii)


We Know,


AO = CO


AO2 = CO2


85 = 4 +


x2 = 324


x = 18 cm

More from this chapter

All 100 →
3

If O is the centre of a circle of radius r and AB is chord of the circle at a distance r/2 from O, then ∠BAO =

 4

ABCD is a cyclic quadrilateral such that ∠ADB =30° and ∠DCA =80°, then ∠DAB =

 6

One chord of a circle is known to be 10 cm. The radius of this circle must be

 7

ABC is a triangle with B as right angle, AC=5 cm and AB = 4 cm. A circle is drawn with A as centre and AC as radius. The length of the chord of this circle passing through C and B is