回復 1# tsyr 的帖子
(1) 因四點共圓，\(\angle BPD=180{}^\circ -\angle B{{I}_{B}}D=\angle {{I}_{B}}BD+\angle {{I}_{B}}DB\) ；\(\angle CPD=180{}^\circ -\angle C{{I}_{C}}D=\angle {{I}_{C}}CD+\angle {{I}_{C}}DC\)
(2) 由餘弦定理，\(\angle A=60{}^\circ =360{}^\circ -2\left( \angle {{I}_{B}}BD+\angle {{I}_{B}}DB+\angle {{I}_{C}}CD+\angle {{I}_{C}}DC \right)\) ,
故\(\angle {{I}_{B}}BD+\angle {{I}_{B}}DB+\angle {{I}_{C}}CD+\angle {{I}_{C}}DC=150{}^\circ \)
(3) \(\angle BPC=\angle BPD+\angle CPD=\angle {{I}_{B}}BD+\angle {{I}_{B}}DB+\angle {{I}_{C}}CD+\angle {{I}_{C}}DC=150{}^\circ \)
(4) 接下來不難驗證等腰三角形時會產生最大面積，此時面積為\(98-49\sqrt{3}\)
