这道题目的解是什么---**Problem Description:** 27. (Total score for this problem is 12 points) As shown in the figure, the quadrilateral ABCD has its diagonal AC as the diameter of circle O, which intersects AB at point K, where arc DC = arc CK, and AC² = AB ⋅ AD. (1) If ∠DAB = 60°, find the measure of ∠DCA; (2) Prove: CB is tangent to circle O; (3) If E is the midpoint of AB, connect CE, DE, let DE intersect AC at point F, and AD = 6, AB = 10, find the value of AC/AF. **Partial Solution (Start):** 解: ∠DAB = 60°. **Diagram Description:** * **Type:** Geometric figure illustrating a quadrilateral inscribed (partially) in a circle and tangent lines. * **Main Elements:** * **Circle O:** A circle with center O and diameter AC. Points A, C, D, K are on the circle. * **Quadrilateral ABCD:** Vertices A, B, C, D. * **Points:** * A, C: Endpoints of the diameter of the circle and vertices of the quadrilateral. * O: Center of the circle, midpoint of AC. * D: Vertex of the quadrilateral, on the circle. * K: Intersection of the circle and the line segment AB. * E: Midpoint of AB. * F: Intersection of line segment DE and AC. * B: Vertex of the quadrilateral, outside the circle. * **Lines/Segments:** * AC: Diameter of the circle, diagonal of the quadrilateral. * AB: Side of the quadrilateral, intersects the circle at K, contains E. * AD, DC, CB: Sides of the quadrilateral. * DE: Line segment connecting D and E, intersects AC at F. * CE: Line segment connecting C and E. * CK, DK: Chords of the circle. * **Arcs:** Arc DC and Arc CK are shown on the circle. The condition states they are equal in measure or length. * **Relative Position and Direction:** * Circle O has AC as its diameter. * Points A, K, E, B are collinear, in that order from left to right. * Points A, F, O, C are collinear, in that order from left to right. * Point F is on the segment AC, between A and C. * Line segment DE passes through F and connects D and E. * Line segment CB is drawn from C to B, and appears tangent to the circle at C. * **Labels:** Points A, B, C, D, O, E, F, K are labeled. The label "第 27 题图" is below the diagram. **Additional Information:** * The problem includes given conditions about arcs and lengths: arc DC = arc CK, AC² = AB ⋅ AD, AD = 6, AB = 10. * Angles mentioned: ∠DAB, ∠DCA. * Length ratio to find: AC/AF.