Question

Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the distance between AB and CD.

• A. 10 cm
• B. 7 cm
• C. 8 cm
• D. 11 cm

Answer 1

The correct option is B

7 cm

Drop perpendiculars OE and OF from O on AB and CD respectively.

Applying Pythagoras' theorem to $\Delta OEB$,

${OE}^2$ + ${BE}^2$ = ${OB}^2$

${OE}^2$ = 25 - 9 (perpendicular drawn from the centre to a chord bisects the chord and hence BE = 3cm)

$\therefore OE$= 4 cm

Similarly, applying Pythagoras' theorem to $\Delta OFD$,

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

${OF}^2$ = 25 - 16

$\Rightarrow OF=3$ cm

So, $EF=OE+OF$ = 4 + 3 = 7 cm