Asked by BWB
Which point(s) of concurrency in a triangle is (are)never outside the triangle?
Is the orthocenter the only concurrency point that stays inside a triangle?
Is the orthocenter the only concurrency point that stays inside a triangle?
Answers
Answered by
Reiny
Actually the orthocentre could be either inside or outside,
if acute angled triangle, ---> inside
if obtuse angled triangle --> outside
http://www.google.ca/imgres?imgurl=http://www.mathwords.com/o/o_assets/orthocenter_obtuse.jpg&imgrefurl=http://www.mathwords.com/o/orthocenter.htm&h=294&w=340&sz=14&tbnid=VX63Op8LOppG1M:&tbnh=103&tbnw=119&prev=/images%3Fq%3Dorthocenter&hl=en&usg=__kUd6Go8Yc4_u7ltGTxIIhqTafE0=&ei=8j7pS6_kIMP58AbPlq3sDg&sa=X&oi=image_result&resnum=8&ct=image&ved=0CD0Q9QEwBw
the incentre, which is the angle bisector intersection, and the centroid are the only ones that stay inside
if acute angled triangle, ---> inside
if obtuse angled triangle --> outside
http://www.google.ca/imgres?imgurl=http://www.mathwords.com/o/o_assets/orthocenter_obtuse.jpg&imgrefurl=http://www.mathwords.com/o/orthocenter.htm&h=294&w=340&sz=14&tbnid=VX63Op8LOppG1M:&tbnh=103&tbnw=119&prev=/images%3Fq%3Dorthocenter&hl=en&usg=__kUd6Go8Yc4_u7ltGTxIIhqTafE0=&ei=8j7pS6_kIMP58AbPlq3sDg&sa=X&oi=image_result&resnum=8&ct=image&ved=0CD0Q9QEwBw
the incentre, which is the angle bisector intersection, and the centroid are the only ones that stay inside
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