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Question Number 19794 by Tinkutara last updated on 15/Aug/17

$$\mathrm{In}\mathrm{a}\mathrm{triangle}ABC\mathrm{with}\mathrm{\angle }BCA=90°,$$$$\mathrm{the}\mathrm{perpendicular}\mathrm{bisector}\mathrm{of}AB$$$$\mathrm{intersects}\mathrm{segments}AB\mathrm{and}AC\mathrm{at}X$$$$\mathrm{and}Y,\mathrm{respectively}.\mathrm{If}\mathrm{the}\mathrm{ratio}\mathrm{of}\mathrm{the}$$$$\mathrm{area}\mathrm{of}\mathrm{quadrilateral}BXYC\mathrm{to}\mathrm{the}$$$$\mathrm{area}\mathrm{of}\mathrm{triangle}ABC\mathrm{is}13:18\mathrm{and}$$$$BC=12\mathrm{then}\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{length}\mathrm{of}AC?$$

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