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 Midpoint problem (Posted on 2013-02-03)
O is the circumcenter of acute triangle ABC, H is the Orthocenter. AD is perpendicular to BC, EF is the perpendicular bisector of AO,D,E on the BC. Prove that the circumcircle of triangle ADE passes through the midpoint of OH.

 No Solution Yet Submitted by Danish Ahmed Khan Rating: 3.0000 (1 votes)

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 Some thoughts | Comment 1 of 2
`Let a, b, and c be real numbers greater than zero. define an xy coordinate systemsuch that A=(0,a), B=(-b,0), C=(c,0),D=(0,0), E=(e,0), F=(f,g), H=(0,h),K=(k,0), L=(i,j), M=(m,n), and P=(u,v). Where F, K, L, M, and N are the midpointsof line segments AO, BC, AB, OH, and AErespectively. It is easy, but tedious, to solve for allthe coordinates in terms of a, b, and c. Then all that is needed is to verify that    |PM|^2 = |PD|^2. `

 Posted by Bractals on 2013-02-03 16:16:12

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