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katykantarovska
@katykantarovska
July 2022
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У трикутнику АВС АВ=ВС=2015, кут АВС=36 градусів. Бісектриси АК і СМ перетинаються в точці О. Знайдіть периметр трикутника АМО.
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oganesbagoyan
Verified answer
Дано :AB = BC =2015 ;<ABC =36° ; <BAK =<CAK; <ACM =<BCM ;
O =[AK]
⋂[CM] .
-----------------------------------------------
P(AMO) - ?
<BAC =<BCA = (180
° - <ABC)/2 =(180° - 36°)/2 =144°/2 =72°.
<BCM
=<BCA /2 = 72°./2 =36°
=<ABC
⇒
MC=MB .
<KAC =
<BAC/2
=
<BCA /2
=
<MCA
⇒
OA =OC.
P(AMO)
=AM+MO+OA =AM+MO+OC =AM+MC=AM+MB =
AB =2015
.
2 votes
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Verified answer
Дано :AB = BC =2015 ;<ABC =36° ; <BAK =<CAK; <ACM =<BCM ;O =[AK] ⋂[CM] .
-----------------------------------------------
P(AMO) - ?
<BAC =<BCA = (180° - <ABC)/2 =(180° - 36°)/2 =144°/2 =72°.
<BCM =<BCA /2 = 72°./2 =36° =<ABC ⇒MC=MB .
<KAC =<BAC/2 =<BCA /2 =<MCA ⇒OA =OC.
P(AMO) =AM+MO+OA =AM+MO+OC =AM+MC=AM+MB =AB =2015.