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

• A. 23 cm
• B. 30 cm
• C. 15 cm
• D. None of these

Answer 1

The correct option is B

30 cm

Given that

OB = OD =17

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

EF = 23 cm

Consider $△$OEB

${OE}^2$ = ${OB}^2$ - ${EB}^2$

${OE}^2$ = ${17}^2$ - $8^2$

OE = 15 CM

OF = EF - OE

OF = 23 - 15

OF = 8 cm

${FD}^2$ = ${OD}^2$ - ${OF}^2$

${FD}^2$ = ${17}^2$ - $8^2$

FD = 15

Therefore CD = 2FD = 30 cm