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2023 BIMC keystage3-IWYMIC team Question 5

xIMC · 2023 BIMC keystage3-IWYMIC team

Question 5

Let $ABC$ be a triangle with $\angle C=90^\circ$, $AC=28$ cm and $BC=14$ cm. Squares $ACDE$ and $BCFG$ are constructed outside the triangle $ABC$. Let $BE$ intersect $AC$ and $AG$ at $H$ and $I$, respectively. $AG$ intersects $BC$ at $J$, as shown in the diagram below. What is the area, in $\mathrm{cm}^2$, of quadrilateral $CHIJ$?

Question illustration