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orthocenter

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A cyclic quadrilateral 2014-03-28
From Carly:
Suppose ABCD is a cyclic quadrilateral, i.e A, B, C, and D are the points on a circle, given in order going around the circle. Show that if we join each of A, B, C, and D to the orthocentre of the triangle formed by the other three, then the resulting line segments all intersect in a common midpoint.
Thank you.

Answered by Chris Fisher.
The circumcentre and orthocentre of a triangle 2012-04-25
From Nazrul:
The circumcentre and orthocentre of a triangle is given. A point on a side of the triangle given. A vertex of the triangle on the circumcircle is also given. How can I draw the triangle? Please Help me. Thank you for answering my previous questions.
Answered by Chris Fisher.
The orthcentre and the circumcentre 2007-04-05
From Ruby:
I have tried to do this question so many times, could you please, please, please show me how to do it. I just can't get the answer: What is the (i)Circumcentre and (ii)Orthocentre of the triangle with vertices a(-2,2) b(2,-6) c(5,3)? It would be so great if you could show me how to do this. Thanks in advance, Ruby.
Answered by Penny Nom.
The orthocentre 2002-10-17
From Elsie:
  1. Find the orthocentre of the triangle with vertices at A(-3,4), B(10, -3) and C(3,-2).

  2. Find the distance of point X(3,8) from the line that passes through Y(-2, -2) and Z (3, -2).

Answered by Chris Fisher.
A geometry proof 2001-04-18
From Melissa:
Extend the bisectors of angle A, angle B, and angle C of triangle ABC to meet the circumcircle at points X, Y, and Z respectively. Show that I is the orthocenter of triangle XYZ.
Answered by Chris Fisher.
 
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