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Inscribe Right Triangle (Posted on 2010-07-18) Difficulty: 3 of 5

Let Q be a point on side BC of triangle ABC.

Construct points P and R on sides AB and AC
respectively such that PQR is a right angle
and PR is parallel to BC.

See The Solution Submitted by Bractals    
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Some Thoughts Thoughts Comment 1 of 1

Segment PR is a diameter of a circle with points P, Q, and R.  The center of that circle then bisects PR, and since PR is parallel to BE, the center lies on the median from vertex A to side BC.

If I knew the radius, then I cound draw the median and draw a circle centered at Q.  The intersection inside the triangle would be the center of the circle containing P, Q, and R.  That circle would intersect AC and BC at P and R.

  Posted by Brian Smith on 2010-07-20 15:39:58
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