<prompt> Pembetatu ABC ina AC 450 na BC 300. Pointi K na L ziko kwenye overlineAC na overlineAB mtawalia ili AK CK, na overlineCL ni kipeo cha pembe mbili cha pembe C . Acha P iwe mahali pa makutano ya overlineBK na overlineCL, na M iwe kielelezo kwenye mstari BK ambayo K ndio kitovu cha muhtasariPM. Ikiwa AM 180, pata LP.asy alama za kuagiza; defaultpenfontsize8; ukubwa 300; jozi A0,0, B30sqrt331,0, C, K, L, M, P; C sehemu za makutanoMduaraA,450, MduaraB,3000; K katikatiA--C; L 3B2A5; P kiendeleziB,K,C,L; M 2K-P; kuchoraA--B--C--mzunguko; choraC--L;choraB--M--A; alaman1,radius15,A,C,L,alamaalama ya mudafremu ya fimbon1,kweli; alaman1,radius15,L,C,B,alamaalama ya mudafremu ya fimbon1,kweli; nuktaABCKLMP; leboA,A,-1,-1;leboB,B,1,-1;leboC,C,1, 1; leboK,K,0,2;leboL,L,0,-2;leboM,M,-1,1 ; leboP,P,1,1; lebo180,AM2,-1,0; lebo180,PC2,-1,0;lebo225 ,AK2,0,2;lebo225,KC2,0,2; lebo300,BC2,1,1; asy  <response>: asy alama za kuagiza; defaultpenfontsize8; ukubwa 300; jozi A0,0, B30sqrt331,0, C, K, L, M, P; C sehemu za makutanoMduaraA,450, MduaraB,3000; K katikatiA--C; L 3B2A5; P kiendeleziB,K,C,L; M 2K-P; kuchoraA--B--C--mzunguko; choraC--L;choraB--M--A; alaman1,radius15,A,C,L,alamaalama ya mudafremu ya fimbon1,kweli; alaman1,radius15,L,C,B,alamaalama ya mudafremu ya fimbon1,kweli; nuktaABCKLMP; leboA,A,-1,-1;leboB,B,1,-1;leboC,C,1, 1; leboK,K,0,2;leboL,L,0,-2;leboM,M,-1,1 ; leboP,P,1,1; lebo180,AM2,-1,0; lebo180,PC2,-1,0;lebo225 ,AK2,0,2;lebo225,KC2,0,2; lebo300,BC2,1,1; asyKwa kuwa K ni kitovu cha overlinePM na overlineAC, quadrilateral AMCP ni paralelogramu, ambayo inamaanisha AMLP na bigtriangleupAMB inafanana. hadi bigtriangleupLPBHivyo,frac AMLPfrac ABLBfrac ALLBLBfrac ALLB1Sasa hebu tutumie nadharia ya pembe mbili.frac ALLBfrac ACBCfrac 450300frac 32frac AMLPfrac ALLB1frac 52frac 180LPfrac 52LP072. 