Let K be a body in the plane and let \(\lambda <1\) be a positive real number. Suppose that for every \(x\in \mathbb R^2\) such that \(\lambda K + x\) is exteriorly tangent to K, the common support cone of K and \(\lambda K + x\) has a constant angle \(\alpha \). Suppose that one of the following conditions is satisfied: (a) K is a body of constant width, (b) K is centrally symmetric. Then K is a Euclidean disc.

中文翻译：

---

通过支撑锥的角度表征圆盘

令K为平面中的一个物体，并令\(\lambda <1\)为正实数。假设对于每个\(x\in \mathbb R^2\)使得\(\lambda K + x\)与K外切，K和\(\lambda K + x\)的公共支撑锥有一个恒定的角度\(\alpha \)。假设满足以下条件之一：(a) K是等宽的物体，(b) K是中心对称的。那么K是欧几里得圆盘。