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SMO 2022 Senior Round 1 Question 11

SMO · SMO 2022 Senior Round 1

Question 11

The figure below shows a quadrilateral $ABCD$ such that $AC=BD$ and $P$ and $Q$ are the midpoints of the sides $AD$ and $BC$ respectively. The lines $PQ$ and $AC$ meet at $R$ and the lines $BD$ and $AC$ meet at $S$. If $\angle PRC=130^\circ$, find the angle $\angle DSC$ (in $^\circ$).

Question illustration