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Triangles
RD Sharma
CBSE
Grade 10

Question:

In $\Delta ABC$, $AD \parallel BC$? No: In trapezium $ABCD$ with $AB \parallel CD$, diagonals intersect at $O$. If $AB = 2 CD$, find the ratio of lengths $AO : OC$.

Step-by-Step Solution

Key Concept: $\Delta AOB \sim \Delta COD \Rightarrow \dfrac{AO}{OC} = \dfrac{AB}{CD} = \dfrac{2CD}{CD} = \dfrac{2}{1} = 2 : 1$.
In $\Delta AOB$ and $\Delta COD$, $\angle AOB = \angle COD$ and $\angle OAB = \angle OCD \Rightarrow \Delta AOB \sim \Delta COD$. [1.5 Marks]
$\dfrac{AO}{OC} = \dfrac{AB}{CD} = \dfrac{2CD}{CD} = 2 : 1$. [1.5 Marks]

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🎯 Official CBSE Marking Scheme:
Proving $\Delta AOB \sim \Delta COD$: 1.5 Marks
Evaluating ratio $AO : OC = 2 : 1$: 1.5 Marks

Correct Answer:
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