5. ∠MKT=◡KM /2 =18° ; ∠OMK =◡KM =2*18° =36°
6. S = AD*h =(AH+HD)*BH =(24+50)*BH =74*BH
ΔAHB:
BH =AH*tgα = 24*tgα , с другой стороны
BH =50*tg( (180 -α)/2) )=50*tg(90° -α/2) =50*ctgα/2)
24*tgα =50*ctg(α/2)
24*tg(α/2) /(1 -tg²(α/2) =25*ctg(α/2)
24*ctg(α/2) /( ctg²(α/2) -1)=25*ctg(α/2) ;
24 =25*ctg²(α/2) - 25 ; ctg(α/2) =7/5
h =50*ctg(α/2) =50*7/5 = 70
S =74*h = 74*70 = 5180
7. S(ΔABC) /S(ABCD) =(BC*h/2) / (AD+BC )*h/2 =BC/(AD+BC)=1/(1+3) =1/4
S(ΔABC) = (1/4)*48 =12.