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Question Number 61952 by lalitchand last updated on 12/Jun/19

Commented by lalitchand last updated on 12/Jun/19

question number 3 prove that

$$\mathrm{question}\:\mathrm{number}\:\mathrm{3}\:\mathrm{prove}\:\mathrm{that}\: \\ $$

Answered by MJS last updated on 12/Jun/19

∠PAC=180°−α ⇒ ∠CAQ=90°−(α/2)  ∠RCA=180°−γ ⇒ ∠ACQ=90°−(γ/2)  ⇒ ∠AQC=((α+γ)/2)   β=180°−(α+γ) ⇒ (α+γ)=180°−β  ⇒ ∠AQC=90°−(β/2)

$$\angle{PAC}=\mathrm{180}°−\alpha\:\Rightarrow\:\angle{CAQ}=\mathrm{90}°−\frac{\alpha}{\mathrm{2}} \\ $$$$\angle{RCA}=\mathrm{180}°−\gamma\:\Rightarrow\:\angle{ACQ}=\mathrm{90}°−\frac{\gamma}{\mathrm{2}} \\ $$$$\Rightarrow\:\angle{AQC}=\frac{\alpha+\gamma}{\mathrm{2}}\: \\ $$$$\beta=\mathrm{180}°−\left(\alpha+\gamma\right)\:\Rightarrow\:\left(\alpha+\gamma\right)=\mathrm{180}°−\beta \\ $$$$\Rightarrow\:\angle{AQC}=\mathrm{90}°−\frac{\beta}{\mathrm{2}} \\ $$

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