Question Number 61952 by lalitchand last updated on 12/Jun/19
Commented by lalitchand last updated on 12/Jun/19
$$\mathrm{question}\:\mathrm{number}\:\mathrm{3}\:\mathrm{prove}\:\mathrm{that}\: \\ $$
Answered by MJS last updated on 12/Jun/19
$$\angle{PAC}=\mathrm{180}°−\alpha\:\Rightarrow\:\angle{CAQ}=\mathrm{90}°−\frac{\alpha}{\mathrm{2}} \\ $$$$\angle{RCA}=\mathrm{180}°−\gamma\:\Rightarrow\:\angle{ACQ}=\mathrm{90}°−\frac{\gamma}{\mathrm{2}} \\ $$$$\Rightarrow\:\angle{AQC}=\frac{\alpha+\gamma}{\mathrm{2}}\: \\ $$$$\beta=\mathrm{180}°−\left(\alpha+\gamma\right)\:\Rightarrow\:\left(\alpha+\gamma\right)=\mathrm{180}°−\beta \\ $$$$\Rightarrow\:\angle{AQC}=\mathrm{90}°−\frac{\beta}{\mathrm{2}} \\ $$