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Australian AMC 2018 - Senior Question 27

AMC AUSTRALIA · Australian AMC 2018 - Senior

Question 27

The trapezium $ABCD$ has $AB=100$, $BC=130$, $CD=150$ and $DA=120$, with right angles at $A$ and $D$.

An interior point $Q$ is joined to the midpoints of all 4 sides. The four quadrilaterals formed have equal areas.

What is the length $AQ$?

Question illustration