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文[1]中,胡如松先生提出了如下猜想,现予以证明.设△DEF为△ABC内接三角形(如图).并设△ABC的三内角为A,B,C;三边BC=a,CA=b,AB=c;EF=a0,FD=b0,DE=c0.分别设△ABC,△DEF,△AEF,△BDF,△CDE的外接圆半径、内切圆半径、半周长和面积依次为R,R0,R1,R2,R3;r,r0,r1,r2,r3;P,P0,P1,P2,
In [1], Mr. Hu Rusong proposed the following conjecture, and we prove it now. Let △ DEF be the inner triangle of △ ABC (pictured), and set the three internal angles of △ ABC as A, B and C; , CA = b, AB = c; EF = a0, FD = b0, DE = c0. Set the circumscribed circle radius, inscribed circle radius, half circumference and The area is R, R0, R1, R2, R3; r, r0, r1, r2, r3;