本文将给出圆锥曲线焦点三角形的内(旁)切圆的两个性质及其应用.定理1.1双曲线的焦点三角形的内切圆与实轴切于顶点.证明如图1,设P是双曲线xa22-by22=1(a0,b0)右支上一点,⊙I是焦点三角形△PF1F2的内切圆,E1、E2、H是切点.由切线长定理,得|PE1|=|PE2|,|F1E1|=|F1H|,|F2H|=|F2 This paper will give two properties of the inner (adjacent) tangent circle of the conic curve focal triangle and its application. Theorem 1.1 The inscribed circle and the real axis of the hyperbola focal triangle are tangent to the vertex. Prove that in Figure 1, let P be double The curve xa22-by22=1(a0,b0) is the point on the right branch, ⊙I is the inscribed circle of the focus triangle ΔPF1F2, E1, E2, H is the tangent point. From the tangent length theorem, we get |PE1|=|PE2| ,|F1E1|=|F1H|,|F2H|=|F2