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#1 2016-07-20 21:40:14

jacks
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Registered: 2012-11-21
Posts: 132

triangles

The number of triangle which are obtuse and points

are the feet of

perpendiculars drawn from vertices on the opposite sides is

Last edited by jacks (2016-07-20 21:40:33)

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#2 2016-07-21 00:27:48

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Registered: 2016-04-16
Posts: 1,086

Re: triangles

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#3 2016-07-21 20:13:45

jacks
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Registered: 2012-11-21
Posts: 132

Re: triangles

Yes Thickhead, Yould you like to explain me , Thanks

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#4 2016-07-21 22:38:29

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Registered: 2016-04-16
Posts: 1,086

Re: triangles

If we join L,M and N the feet of perpendiculars from A,B,c to opposite sides to form a triangle it is known that the in center of this triangle is the ortho center of ABC. This only applies to acute angle triangle ABC. If ABC is obtuse then the orthocenter of ABC lies outside LMN but a circle can be drawn from ortocenter touching one side of LMN  and the other two  extended sides. Thus there will be 3 configurations for obtuse angled triangle.

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#5 2016-07-22 02:57:11

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Registered: 2016-04-16
Posts: 1,086

Re: triangles

the 3 outcenters (as compared to in centers) are (50,-5) (5,10)(15,30) incenter is (10,15)
for (50,-5) The triangle ABC will have vertices A(5,10) B(10,15) C(15,30) the angles are

by using wolfram alpha widgets. Others I have not tried.It is surprising that when I have chosen one from the first line as orthocenter the other 3 have become vertices.

Last edited by thickhead (2016-07-22 22:30:17)

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#6 2016-07-23 21:23:58

jacks
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Registered: 2012-11-21
Posts: 132