Geometry Problem

Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to see the complete problem 977.

## Sunday, February 9, 2014

### Geometry Problem 977: Acute Triangle, Circumcenter, Orthocenter, Distance, Circumradius, Altitude, Metric Relations

Labels:
acute,
altitude,
circumcenter,
circumradius,
distance,
metric relations,
orthocenter,
triangle

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BD cut circle O at E

ReplyDeleteSince H is the orthocenter of triangle ABC => HD=HE

Power of point H to circle O= -HB.HE=d^2-R^2

but HE=2.HD => d^2=R^2-2.HD.HB