Cho tam giác $ABC.$ Các tia phân giác của các góc $B$ và $C$ cắt nhau ở $O.$ Kẻ OD⊥AC" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">OD⊥AC$\mathrm{O}\mathrm{D}\mathrm{\perp }AC$, kẻ OE⊥AB" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">OE⊥AB$\mathrm{O}E\mathrm{\perp }AB$. Chứng minh rằng $OD=OE.$

Cho tam giác $ABC$ có B^=C^" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">ˆB=ˆC$\hat{B}=\hat{C}$. Tia phân giác góc $A$ cắt $BC$ tại $D.$ Chứng minh rằng $DB=DC,AB=AC.$

Cho biết hai đại lượng x và y tỉ lệ nghịch với nhau. Điền số thích hợp vào ô trống trong bảng sau:

Cho đa thức $P\left(x\right)=x^2+mx-9$(m là tham số).
a/ Tìm giá trị của m để $x=1$ là một nghiệm của đa thức $P\left(x\right)$.
b/ Khi $m=0$, tìm tất cả các nghiệm của đa thức $P\left(x\right)$.
c/ Khi $m=0$, tìm giá trị nhỏ nhất của đa thức $P\left(x\right)$.

Cho tam giác $ABC$ có B^=C^=50∘" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">ˆA=ˆB=60∘$\hat{B}=\hat{C}={50}^{\circ }$. Gọi tia Cx$Am$ là tia phân giác của góc ngoài ở đỉnh $C.$ Hãy chứng tỏ //BC" role="presentation" style="border:0px; direction:ltr; display:inline-table; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">AB//Cx$Am//BC$.

$Cho$ ΔMNP" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">ΔMNP$\mathrm{\Delta }MNP$ ó" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">có$có$ M^=30o" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">ˆM=30o$\hat{M}={30}^o$$;$ N^=20o" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">ˆN=20o$\hat{N}={20}^o$$.$ ên" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">Trên$Trên$ $MN$ ấy" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">lấy$lấy$ $D$ $sao$ $cho$ $MD=NP$$.$ ính" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">Tính$Tính$ NPD^" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:20.34px; font-style:normal; font-weight:normal; letter-spacing:normal; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; text-align:left; text-indent:0px; text-transform:none; white-space:nowrap; word-spacing:normal" class="MathJax_CHTML mjx-chtml">ˆNPD$\widehat{NPD}$ $.$

Cho y = $\frac{x.\left|x-2\right|}{x-2}$ , x $\ne$ 2 . Rút gọn y và tính giá trị của y khi x = 2019

Cho a,b∈R;n∈N∗" role="presentation" style="border:0px; color:rgb(40, 40, 40); direction:ltr; display:inline-block; float:none; font-family:helvetica,arial,sans-serif; font-size:16.38px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; padding:1px 0px; position:relative; white-space:nowrap; word-wrap:normal" class="MathJax_CHTML mjx-chtml">a,b∈R;n∈N∗${\displaystyle a,b\in R;n\in N^{\ast }}$. Chứng minh rằng:

Cho tam giác $ABC$ có B^=C^=50∘" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; font-family:arial,tahoma,helvetica,sans-serif; font-size:18.72px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">ˆA=ˆB=60∘$\hat{B}=\hat{C}={50}^{\circ }$. Gọi tia $Am$ là tia phân giác của góc ngoài ở đỉnh $\mathrm{C.}$ Hãy chứng tỏ //BC" role="presentation" style="border:0px; direction:ltr; display:inline-block; float:none; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap" class="MathJax_CHTML mjx-chtml">Cx/
/AB.