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 .....

Question

Philoid · Accepted 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,

⇒ OB² = OM² + MB²

⇒ 5² = OM² + 3²

⇒ OM² = 25-9

⇒ OM² = 16

⇒ OM = 4cm

In ΔONC,

⇒ OC² = ON² + CN²

⇒ 5² = ON² + 4²

⇒ ON² = 25-16

⇒ ON² = 9

⇒ ON = 3cm

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

Hence the correct option is D.

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 .....