<prompt> asy unitsize27; defaultpenlinewidth.8ptfontsize10pt; jozi A,B,C,D,E,F,X,Y,Z; A3,3; B0,0; C6,0; D4,0; E4,2; F1,1; kuchoraA--B--C--mzunguko; kuchoraA--D; kuchoraB--E; kuchoraC--F; XintersectionpointA--D,C--F; YintersectionpointB--E,A--D; ZintersectionpointB--E,C--F; leboA,A,N; leboB,B,SW; leboC,C,SE; leboD,D,S; leboE,E,NE; leboF,F,NW; leboN_1,X,NE; leboN_2,Y,WNW; leboN_3,Z,S; asyKatika takwimu, overlineCD, overlineAE na overlineBF ni theluthi moja ya pande zao. Inafuata kwamba overlineAN_2: overlineN_2N_1: overlineN_1D 3: 3: 1, na vile vile kwa mistari BE na CF. Kisha eneo la pembetatu N_1N_2N_3 ni:textA frac 110 pembetatu ABC qquad textB frac 19 pembetatu ABC qquad textC frac 17pembetatu ABCqquad textD frac16pembetatu ABCqquad textE texthakuna kati ya hizi  <response>: Acha ABCK. Kisha ADC frac13K, na hivyo N_1DC frac17 ADC frac1 21K. Vile vile, N_2EAN_3FB frac121K. Kisha N_2N_1CE ADC - N_1DC-N_2EA frac5 21K, na sawa kwa pande za pembe nne. Kisha N_1N_2N_3 ni ABC tu ukiondoa maeneo mengine yote ambayo tumekokotoa. Hiyo ni,N_1N_2N_3 K - 3kushotofrac121Kkulia - 3kushotofrac521kuliaK K - frac 67K frac17pembetatu ABC. 