解这道题---**Textual Information** 已知：△ABC 外接于 ⊙O，∠BAC = 60°，AE ⊥ BC，CF ⊥ AB，AE、CF 相交于点 H，点 D 为弧 BC 的中点，连接 HD、AD。求证：△AHD 为等腰三角形 简证：易证 ∠BHC = 120°，∠BOC = 120°，∴ B、H、O、C 四点共圆。 DB = DO = DC，∴ DH = DO = OA，又 AH ∥ OD，∴ AHDO 是菱形 ∴ AH = HD，△AHD 为等腰三角形。 **Chart Description** * **Type:** Geometric diagram illustrating a triangle inscribed in a circle, with altitudes and other related points and segments. * **Main Elements:** * A circle labeled with center O. * A triangle △ABC with vertices A, B, C lying on the circle. * Line segment AE drawn from A perpendicular to BC at point E. * Line segment CF drawn from C perpendicular to AB at point F. * Point H is the intersection of AE and CF (the orthocenter of △ABC). * Point D is located on the arc BC (presumably the major arc based on the position, and specified as the midpoint of arc BC). * Line segments HD and AD are drawn (solid lines). * Line segments OA, OB, OC, OD, OE, OF, OH are drawn (some solid, some dashed). * Point labels A, B, C, D, E, F, H, O are present at their respective locations. * **Lines/Segments:** * Solid lines: AB, BC, CA, AE, CF, HD, AD. * Dashed lines: OB, OC, OA, OD, OH, OE, OF. * **Relationships:** * AE is perpendicular to BC. * CF is perpendicular to AB. * AE and CF intersect at H. * D is the midpoint of arc BC. * O is the center of the circle containing A, B, C, D. * The diagram illustrates the configuration described in the problem statement.