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Question Number 184655 by Mastermind last updated on 10/Jan/23

$$\mathrm{prove}\mathrm{that}\mathrm{an}\mathrm{angle}\mathrm{inscribe}\mathrm{in}\mathrm{a}$$$$\mathrm{semi}-\mathrm{circle}\mathrm{is}\mathrm{a}\mathrm{right}\mathrm{angle}.$$$$$$$$$$$$\mathrm{Help}!$$

Answered by HeferH last updated on 10/Jan/23

Commented by HeferH last updated on 10/Jan/23

$$\stackrel{⌢}{AB}=180°$$$$\mathrm{\angle }ACB=\frac{\stackrel{⌢}{AB}}{2}=90°\left(inscribedangletheorem\right)$$

Commented by HeferH last updated on 10/Jan/23

Commented by HeferH last updated on 10/Jan/23

$$2\alpha +2\theta +(180°-2\theta -\beta )=180°$$$$\beta =2\alpha$$

Commented by Mastermind last updated on 10/Jan/23

$$\mathrm{What}\mathrm{is}\mathrm{this}\mathrm{one}\mathrm{again}?$$

Commented by Mastermind last updated on 10/Jan/23

$$\mathrm{Thank}\mathrm{you}\mathrm{BOSS}$$

Commented by HeferH last updated on 10/Jan/23

$$ProofoftheInscribedangletheorem:)$$

Commented by Mastermind last updated on 10/Jan/23

$$\mathrm{Thank}\mathrm{you}\mathrm{BOSS}\mathrm{but}\mathrm{i}\mathrm{think}\mathrm{the}$$$$\mathrm{first}\mathrm{one}\mathrm{is}\mathrm{the}\mathrm{corrct}\mathrm{solution}$$

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