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In the given figure, $AO OC = BO OD = 12$ and $AB = 5 cm .$ , then the value of $DC$ is,

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5 cm

10cm

15cm

20cm

answer is B.

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Detailed Solution

Given figure is,
In figure, AO / OC = BO / OD =1/2 and AB =5 cm. Find the value of DC .

It is given that the ratio of the corresponding sides of the triangles are equal that is,

A O O C = B O O D = 12

As the angles,

∠ A O B

and

∠ C O B

are vertically opposite angles.
So, they are also equal.
Therefore, the triangles

Δ

AOB and

Δ

COB are similar by SAS pattern.
Therefore,

B O O D = A B D C ⇒ 12 = 5 D C ⇒ D C = 10 cm

Hence, the value of DC is 10cm.
Hence, option 2 is correct.

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