To find length, don't always search for length

Geometry Level 2

$ABCD$ is a trapezoid where $AB$ is parallel to $DC$ . The diagonals $AC$ and $BD$ intersect each other at $O$ . Given that $OA=5$ , $OD=6$ , $OC=3$ , find $OB$ .

The answer is 10.

2 solutions

Vaibhav Prasad
Apr 16, 2015

$AO \times OD = OC \times OB \\ \rightarrow \frac{5 \times 6}{3} = 5 \times 2 =\boxed {10}$

Which theorem is this ?

Aman Real - 6 years, 1 month ago

It follows from similar triangles $DOC$ and $AOB$ .

lawrence Bush - 6 years, 1 month ago

Sides of similar triangles are always in ratio.

A Former Brilliant Member - 5 years, 12 months ago

Hey @Vaibhav Prasad you need to show that triangle $ODC$ & $OAB$ are similar!

Harsh Shrivastava - 6 years, 1 month ago

not necessarily directly take ratio of diagonals

A Former Brilliant Member - 5 years, 12 months ago

Atanu Ghosh
Feb 19, 2016

atanughosh253

So GUYS, You will able to see that ▲AOB is similar to ▲COD, so their ratio of corresponding sides will equal. Then you will able to find the ANSWER. So the ANSWER IS 10(TEN) Units.

To find length, don't always search for length

The answer is 10.

2 solutions

atanughosh253

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