Question

[Vũ Phương Linh]

CMR:

a, \(r=\frac{a\cdot\sin\frac{B}{2}\cdot\sin\frac{C}{2}}{\cos\frac{A}{2}}\)

b, \(S=\frac{1}{2}\sqrt{\overrightarrow{AB}^2\cdot\overrightarrow{AC}^2}-\left(\overrightarrow{AB}\cdot\overrightarrow{AC}\right)^2\)

Answer 1

[DƯƠNG PHAN KHÁNH DƯƠNG]

b) \(S=\frac{1}{2}\sqrt{AB^2.AC^2-\left(\overrightarrow{AB}.\overrightarrow{AC}\right)^2}\)

\(=\frac{1}{2}\sqrt{AB^2.AC^2-AB^2.AC^2.cos^2A}\)

\(=\frac{1}{2}\sqrt{AB^2AC^2.sin^2A}\)

\(=\frac{1}{2}.AB.AC.\sin A\) (đpcm)