ABC内接于⊙O,P为弧AC的中点,PQ//AB,点Q在BC上,QR//PA,点R在AB上,求证：AR=BQ

Question

ABC内接于⊙O,P为弧AC的中点,PQ//AB,点Q在BC上,QR//PA,点R在AB上,求证：AR=BQ

Answer 1

连结AP,由条件可知：AR=PQ,∠PBC=∠PBA=∠BPQ,则BQ=PQ=AR,故如题所言.