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

10 cm

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7 cm

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8 cm

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11 cm

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Solution

The correct option is B
7 cm

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

Applying Pythagoras' theorem to $Δ O E B$ ,

${O E}^{2}$ + ${B E}^{2}$ = ${O B}^{2}$

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

$∴ O E$ = 4 cm

Similarly, applying Pythagoras' theorem to $Δ O F D$ ,

${O F}^{2}$ + ${F D}^{2}$ = ${O D}^{2}$

${O F}^{2}$ = 25 - 16

$\Rightarrow O F = 3$ cm

So, $E F = O E + O F$ = 4 + 3 = 7 cm

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