See complete Problem 117
Area of Triangles, Incenter, Excircles, Tangent. Level: High School, SAT Prep, College geometry
Post your solutions or ideas in the comments.
Monday, June 9, 2008
Elearn Geometry Problem 117
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name M point P meet AB, T meet AC
ReplyDeletename N point Q meet BC, S meet AC
from P119
S2 = SHIN, S3 = SGIM
have to prove SINC = SIMA or
NC = AM*, because altitude is r for two tr
AS = AE (as tg from A )
AC + CN = AB + BN ( CN=CS ,BE=BN, tg from C, B )
AC + CN = AM + MB + BC - CN ( AB = AM+MB, BN = BC-CN)
AC + CN = AM + AC + AM - CN ( MB+BC = AC+AM = 1/2p )
2∙CN = 2∙AM
CN = AM*
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(area of IAE) = (area of ICD)= (1/2)(area of ABC).
ReplyDeleteSubtract (area of IGBH) from both sides.