1.
\((1)\)
如图,\(⊙O\)中\(\overset\frown{AB}\)的中点为\(P\),弦\(PC\),\(PD\)分别交\(AB\)于\(E\),\(F\)两点.
\((I)\)若\(∠PFB=2∠PCD\),求\(∠PCD\)的大小;
\((II)\)若\(EC\)的垂直平分线与\(FD\)的垂直平分线交于点\(G\),证明\(OG⊥CD\).
\((2)\) 在直角坐标系\(xOy\)中,曲线\({C}_{1} \)的参数方程为\(\begin{cases}x= \sqrt{3}\cos θ \\ y=\sin θ\end{cases} (θ \)为参数\()\),以坐标原点为极点,以\(x\)轴的正半轴为极轴,,建立极坐标系,曲线\({C}_{2} \)的极坐标方程为\(ρ\sin (θ+ \dfrac{π}{4})=2 \sqrt{2} \).
\((I)\)写出\({C}_{1} \)的普通方程和\({C}_{2} \)的直角坐标方程;
\((II)\)设点\(P\)在\({C}_{1} \)上,点\(Q\)在\({C}_{2} \)上,求\(|PQ|\)的最小值及此时\(P\)的直角坐标.
\((3)\) 已知函数\(f(x)=|2x−a|+a \)
\((I)\)当\(a=2\)时,求不等式\(f(x)⩽6 \)的解集;
\((II)\)设函数\(g(x)=|2x−1|, \)当\(x∈R \)时,\(f(x)+g(x)\geqslant 3\),求\(a\)的取值范围