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

Question

Q) In the given figure, $\frac{AO}{OC} = \frac{BO}{OD} = \frac{1}{2}$ and AB = 5 cm. Find the value of DC.

[UP Board Exam paper, 2024]

Sapling Academy · Accepted Answer

Step 1: Lets start with Δ AOB and Δ COD:

If these triangles are similar, then:

$\frac{AO}{OC} = \frac{BO}{OD}$

Since it is given that $\frac{AO}{OC} = \frac{BO}{OD}$ ,

Therefore, by SAS criterion of similarity, Δ AOB $\sim$ Δ COD

Step 2: Since both triangles are similar, then the ratio of equality will also be applicable for the third side as well, and hence,

$\frac{AO}{OC} = \frac{BO}{OD} = \frac{1}{2} = \frac{AB}{CD}$

Step 3: From the last 2 parts, we have:

$\frac{1}{2} = \frac{AB}{CD}$

∴ CD = 2 AB

Since it is given that AB = 5 cm,

∴ CD = 2 x 5 = 10 cm

Therefore, the length of side CD is 10 cm.

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