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Question Number 20545 by Tinkutara last updated on 23/Sep/17

$$\mathrm{Let}\mathrm{ABC}\mathrm{be}\mathrm{an}\mathrm{acute}-\mathrm{angled}\mathrm{triangle}$$$$\mathrm{with}\mathrm{AC}\ne \mathrm{BC}\mathrm{and}\mathrm{let}\mathrm{O}\mathrm{be}\mathrm{the}$$$$\mathrm{circumcenter}\mathrm{and}\mathrm{F}\mathrm{be}\mathrm{the}\mathrm{foot}\mathrm{of}$$$$\mathrm{altitude}\mathrm{through}\mathrm{C}.\mathrm{Further},\mathrm{let}\mathrm{X}\mathrm{and}$$$$\mathrm{Y}\mathrm{be}\mathrm{the}\mathrm{feet}\mathrm{of}\mathrm{perpendiculars}\mathrm{dropped}$$$$\mathrm{from}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{respectively}\mathrm{to}(\mathrm{the}$$$$\mathrm{extension}\mathrm{of})\mathrm{CO}.\mathrm{Prove}\mathrm{that}\mathrm{FY}\mathrm{\perp }\mathrm{CA}$$$$\mathrm{using}\mathrm{that}\mathrm{\angle }\mathrm{CFY}=\mathrm{\angle }\mathrm{CBY}=\mathrm{\angle }\mathrm{CAF}.$$

Commented by Tinkutara last updated on 23/Sep/17

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