IIMB 2001 (QA) PYQs

In the given diagram, $ABCD$ is a trapezium. If $AB=4$ cm, $CD=6$ cm and $OB=5$ cm, then what is the length of $OD.$

PQRS is a cyclic quadrilateral whose diagonals PR and QS intersect at the point T. $\angle SQR$ measures $72^\circ$, and $\angle QPR$ measures $28^\circ$. What is the measure of $\angle QRS$?

$ABCD$ is a quadrilateral. The diagonals of $ABCD$ intersect at the point $P$. The area of the triangles $APD$ and $BPC$ are $27$ and $12$, respectively. If the areas of the triangles $APB$ and $CPD$ are equal then the area of triangle $APB$ is