Q. 1 G4.3( 12 Votes )

# Choose correct alternative answer and fill in the blanks.

The lengths of parallel chords which are on opposite sides of the center of a circle are 6 cm and 8 cm. If radius of the circle is 5 cm, then the distance between these chords is .....

A. 2 cm

B. 1 cm

C. 8 cm

D. 7 cm

Answer :

Let, length of AB = 6cm and length of CD = 8cm

Radius of circle = 5cm

OB = OC = 5cm

We know that a perpendicular drawn from the center of a circle on its chord bisects

the chord.

AM = MB = 3cm

Also, CN = ND = 4cm

In ΔOMB,

⇒ OB^{2} = OM^{2} + MB^{2}

⇒ 5^{2} = OM^{2} + 3^{2}

⇒ OM^{2} = 25-9

⇒ OM^{2} = 16

⇒ OM = 4cm

In ΔONC,

⇒ OC^{2} = ON^{2} + CN^{2}

⇒ 5^{2} = ON^{2} + 4^{2}

⇒ ON^{2} = 25-16

⇒ ON^{2} = 9

⇒ ON = 3cm

Distance between AB and CD = OM + ON = 4 + 3 = 7cm

Hence the correct option is D.

Rate this question :

In a circle with radius 13 cm, two equal chords are at a distance of 5 cm from the center. Find the lengths of the chords.

In the figure 6.19, C is the center of the circle. seg QT is a diameter CT = 13, CP = 5, find the length of chord RS.

MHB - Math Part-II

Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the center of the circle?

MHB - Math Part-IIIn the figure 6.21, CD is a diameter of the circle with center O. Diameter CD is perpendicular to chord AB at point E. Show that ΔABC is an isosceles triangle.

MHB - Math Part-II