Втреугольнике abc на сторонах ab и bc взяты точки k и m; o - точка пересечения ck и am. обозначим ak/kb=k, bm/mc=m, co/ok=p, ao/om=l. пусть из четырёх чисел k,m,p и l известны два. найдите два оставшихся числа, если: а) k=2, m=1/3; б)k=2/3, m=1/2; в)k=3, p=2; г)k=2; l=3; д)m=1/3,l=1/3; е) p=2, l=1.
AK/AB * BM/MC * CO/OK = 1
2/3 * 1/3 * CO/OK = 1
2/9 * CO/OK = 1
CO/OK = p = 9/2
BK/AK * MC/BC * AO/OM = 1
1/2 * 3/4 * AO/OM =1
3/8 * AO/OM = 1
AO/OM = l = 8/3
б) AK/KB = 2/3 ; BM/MC = 1/2, CO/OK - ? ; AO/OM - ?
AK/AB * BM/MC * CO/OK = 1
2/5 * 1/2 * CO/OK = 1
1/5 * CO/OK = 1
CO/OK = p = 5
BK/AK * MC/BC * AO/OM = 1
3/2 * 2/3 * AO/OM = 1
AO/OM = l = 1
в) AK/KB = 3 ; CO/OK = 2 ; BM/MC - ? , AO/OM - ?
AK/AB * CO/OK * BM/MC = 1
3/4 * 2/1 * BM/MC =1
3/2 * BM/MC =1
BM/MC = m = 2/3
BK/AK * MC/BC * AO/OM = 1
1/3 * 3/5 * AO/OM = 1
1/5 * AO/OM = 1
AO/OM = l = 5
г) AK/KB = 2 ; AO/OM = 3 ; CO/OK - ? ; BM/MC - ?
AM/AO * AB/AK * BM/MC = 1
4/3 * 3/2 * BM/MC = 1
2 * BM/MC = 1
BM/MC = m = 1/2
AK/AB * BM/MC * CO/OK = 1
2/3 * 1/2 * CO/OK = 1
1/3 * CO/OK = 1
CO/OK = p = 3
д) BM/MC = 1/3 ; AO/OM = 1/3; AK/BK - ? ; CO/OK - ?
OM/OA * BC/MC * AK/BK = 1
3/1 * 4/3 * AK/BK = 1
4*AK/BK = 1
AK/BK = k = 1/4
AK/AB * BM/MC * CO/OK = 1
1/5 * 1/3 * CO/OK = 1
1/15 *CO/OK =1
CO/OK = p = 15
е) CO/OK = 2 ; AO/OM = 1; AK/KB - ? ; BM/MC - ?
CK/OK * AO/OM * AK/KB = 1
3/1 * 1/1 * AK/KB = 1
3 * AK/KB = 1
AK/KB = k = 1/3
AK/AB * CO/OK * BM/MC = 1
1/4 * 2/1 * BM/MC = 1
1/2 * BM/MC =1
BM/MC = m = 2