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In the quadrilateral $ABCD$ diagonals $AC$ and BD intersect each other at a point O such that $A O O C = B O O D = 12$ . If $AB = 4 cm$ , find the length of DC.

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12cm

10cm

8cm

4cm

answer is C.

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Detailed Solution

The given information given in the question are,

A O O C = B O O D = 12 A B = 4 c m

.
Let us draw the figure for better understanding.
In the given figure, ABCD is a trapezium in which AB║DC and its diagonals intersect at O. If AO = (5x – 7), OC = (2x + 1) - Sarthaks eConnect | Largest Online Education Community

In the given figure, ABCD is a trapezium in which AB║DC and its diagonals intersect at O. If AO = (5x – 7), OC = (2x + 1) - Sarthaks eConnect | Largest Online Education Community

Since the corresponding sides ratio is already equal, we can write that,

.
Since

Δ O A B ~ Δ O C D

we can write that,

A O O C = B O O D = A B D C A B D C = 12 4 D C = 12 D C = 8 c m

The value is

D C = 8 c m

.
Hence, the correct option is 1.

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