As shown in the figure, the quadrilateral ABCD is inscribed in the circle, the diagonal AC and BD intersect at the point E, f is on AC, ab = ad, ∠ BFC = ∠ bad = 2 ∠ DFC. Verification: (1) CD ⊥ DF; (2) BC = 2CD

As shown in the figure, the quadrilateral ABCD is inscribed in the circle, the diagonal AC and BD intersect at the point E, f is on AC, ab = ad, ∠ BFC = ∠ bad = 2 ∠ DFC. Verification: (1) CD ⊥ DF; (2) BC = 2CD


It is proved that: (1) AB = ad, ∵ arc AB = arc ad, ∵ ADB = ∵ abd. ∵ ACB = ∵ ADB, ∵ ACD = ∵ abd, ∵ ACB = ∵ ADB = ∵ abd = ∵ ACD. ∵ ADB = (180 ° - bad) △ 2 = 90 ° - DFC. ∵ ADB + ∵ DFC = 90 °, i.e.