Question Number 39511 by behi83417@gmail.com last updated on 06/Jul/18
Commented by behi83417@gmail.com last updated on 08/Jul/18
$$\boldsymbol{{in}}\:\boldsymbol{{ABCD}},\boldsymbol{{E}},\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{intersect}}\:\boldsymbol{{point}} \\ $$$$\boldsymbol{{of}}\:\boldsymbol{{diagonals}}.\boldsymbol{{draw}}\:\boldsymbol{{outcircles}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{A}}\overset{\bigtriangleup} {\boldsymbol{{B}E}}\:\boldsymbol{{and}}\:\boldsymbol{{C}}\overset{\bigtriangleup} {\boldsymbol{{D}E}}.\boldsymbol{{say}}\:\boldsymbol{{the}}\:\boldsymbol{{center}}\:\boldsymbol{{of}} \\ $$$$\boldsymbol{{two}}\:\boldsymbol{{circles}}\:\boldsymbol{{as}}:\boldsymbol{{P}}\:\boldsymbol{{and}}\:\boldsymbol{{Q}}. \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}:\:\boldsymbol{{PQ}}\geqslant\frac{\boldsymbol{{AB}}+\boldsymbol{{CD}}}{\mathrm{4}}\:\:. \\ $$
Commented by ajfour last updated on 08/Jul/18
$${Great}\:{Question}\:! \\ $$