Question

In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is ______ 

Options

• None of these

• 15 cm

• 30 cm

• 23 cm

Answer 1

In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is 30 cm.

Explanation:

Given that

OB = OD = 17

AB = 16 ⇒ AE = BE = 8 cm as perpendicular from centre to the chord bisects the chords

EF = 23 cm

Consider ΔOEB

OE² = OB² - EB²

OE² = 17² - 8²

OE = 15 CM

OF = EF - OE

OF = 23 - 15

OF = 8 cm

FD² = OD² - OF²

FD² = 17² - 8²

FD = 15

Therefore CD = 2FD = 30 cm