a/ Xét \(ΔADB\) và \(ΔCDI\):
\(\widehat{DAB}=\widehat{DCI}(gt)\)
\(\widehat{ADB}=\widehat{CDI}\) (đối đỉnh)
\(→ΔADB\backsim ΔCDI(g-g)\)
b/ \(ΔADB\backsim ΔCDI→\widehat{ABD}=\widehat{CID}\) hay \(\widehat{ABD}=\widehat{AIC}\)
Xét \(ΔADB\) và \(ΔACI\):
\(\widehat{ABD}=\widehat{AIC}(cmt)\)
\(\widehat{BAD}=\widehat{IAC}\) (\(AD\) là đường phân giác \(\widehat A\) )
\(→ΔADB\backsim ΔACI(g-g)\)
c/ \(ΔADB\backsim ΔACI→\dfrac{AD}{AB}=\dfrac{AC}{AI}\)
\(↔AB.AC=AD.AI\)
\(ΔADB\backsim ΔCDI→\dfrac{AD}{DB}=\dfrac{CD}{DI}\)
\(↔DB.CD=AD.DI\)
\(AB.AC-DB.DC\\=AD.AI-AD.DI\\=AD.(AI-DI)\\=AD.AD=AD^2\)
\(→\) ĐPCM
