Prove that the 9-point circle bisects every segment connecting the orthocenter to a point on the circumcircle.

Thanks very much for your help!!!! :)

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- April 10th 2006, 08:54 PMsuedenationGeometry
Prove that the 9-point circle bisects every segment connecting the orthocenter to a point on the circumcircle.

Thanks very much for your help!!!! :) - April 11th 2006, 04:06 PMThePerfectHackerQuote:

Originally Posted by**suedenation**

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Draw triangle ABC, then, mark off its midpoints XYZ. Draw triangle XYZ, we can show that XYZ is similar to ABC, by ratio of 2:1. Next, by the Extended law of sine, we know that for the big triangle and for the small triangle. But the sides are in proportion of 2:1 thus, but thet are similar thus, . From here we see .

Any problems? I explained it horrifically.