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Question Number 8618 by Rasheed Soomro last updated on 18/Oct/16

Commented by Rasheed Soomro last updated on 18/Oct/16

$$\mathrm{AD}\mathrm{and}\mathrm{CD}\mathrm{are}\mathrm{tangents}\mathrm{of}\mathrm{the}$$$$\mathrm{circle}.\mathrm{\angle }\mathrm{ABC}\mathrm{is}\mathrm{inscibed}\mathrm{angle}\mathrm{of}$$$$\mathrm{the}\mathrm{arc}\stackrel{⌢}{\mathrm{ABC}}.$$$$\mathrm{\angle }\mathrm{ABC}\left(\alpha \right)=\mathrm{x}°$$$$\mathrm{\angle }\mathrm{ADC}\left(\beta \right)=?$$$$$$

Answered by sandy_suhendra last updated on 18/Oct/16

$$\stackrel{⌢}{\mathrm{AC}}=2\mathrm{x}$$$$\stackrel{⌢}{\mathrm{ABC}}=360°-2\mathrm{x}$$$$\beta =\frac{1}{2}\times (\stackrel{⌢}{\mathrm{ABC}}-\stackrel{⌢}{\mathrm{AC}})=\frac{1}{2}\times (360°-2\mathrm{x}-2\mathrm{x})=180°-2\mathrm{x}$$

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