$A B$ and $C D$ are parallel line segments of lengths $8$ cm and $7$ cm respectively. If $A D$ and $B C$ intersect at $O$ and $A O = 16$ cm, then $O D$ is equal to:

14

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15

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Solution

The correct option is A $14$ cm
From $Δ O A B$ and $Δ O D C$
$∠ A O B = ∠ D O C$ ...(opposite angles)
$∠ D A B = ∠ A D C$ ...(alternate angles)
$∠ C B A = ∠ D C B$ ...(alternate angles)
$∴ Δ O A B$ and $Δ O D C$ are similar.
$\frac{O D}{O A} = \frac{C D}{A B}$
$∴ O D = \frac{O A \times C D}{A B}$
$= \frac{16 \times 7}{8} = 14$ cm
Hence, option A.

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