1983 IMO 第 4 题

(BEL 5) On the sides of the triangle $A B C$, three similar isosceles triangles $A B P(A P=P B), A Q C(A Q=Q C)$, and $B R C(B R=R C)$ are constructed. The first two are constructed externally to the triangle $A B C$, but the third is placed in the same half-plane determined by the line $B C$ as the triangle $A B C$. Prove that $A P R Q$ is a parallelogram.

(BEL 5) 在三角形 $A B C$ 的边上，构造三个相似的等腰三角形 $A B P(A P=P B)、A Q C(A Q=Q C)$ 和 $B R C(B R=R C)$。前两个是在三角形 $A B C$ 的外部构造的，但第三个与三角形 $A B C$ 放置在由线 $B C$ 确定的同一半平面中。证明 $A P R Q$ 是平行四边形。