B D C D = A B sin ∠ B A D A C sin ∠ C A D {\displaystyle {\frac {BD}{CD}}={\cfrac {AB\sin \angle BAD}{AC\sin \angle CAD}}} [1]
分角定理，是平面几何学的一个定理。
S △ A B D S △ A C D = B D C D {\displaystyle {\frac {S_{\triangle ABD}}{S_{\triangle ACD}}}={\frac {BD}{CD}}}
S △ A B D S △ A C D = 1 2 A B ⋅ A D sin ∠ B A D 1 2 A C ⋅ A D sin ∠ C A D = A B sin ∠ B A D A C sin ∠ C A D {\displaystyle {\frac {S_{\triangle ABD}}{S_{\triangle ACD}}}={\cfrac {{\cfrac {1}{2}}AB\cdot AD\sin \angle BAD}{{\cfrac {1}{2}}AC\cdot AD\sin \angle CAD}}={\cfrac {AB\sin \angle BAD}{AC\sin \angle CAD}}}
B D C D = A B sin ∠ B A D A C sin ∠ C A D {\displaystyle {\frac {BD}{CD}}={\cfrac {AB\sin \angle BAD}{AC\sin \angle CAD}}}
