Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.
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Thursday, January 14, 2016
Geometry Problem 1178: Triangle, Internal Angle Bisector, Metric Relations
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Lets assume AD extended meets circumcircle of Tr.ABC at point E.
ReplyDeleteAssuming DE=x, we have d.x= BD.CD
BD = ac/(b+c), CD = ab/(b+c)
Also Tr. ACD is similar to Tr.AEB
We have d/c=b/(d+x) we get
d^2 = bc - dx or d^2 = bc - BD.CD
Substituting values of BD and CD we get required expression.
Perhaps the easiest way of doing this thro' pure geometry alone
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