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The figure shows an arbelos ABC (AB, BC, and AC are semicircles), BD is perpendicular to AC and chord EF is the common external tangent to semicircles AB and BC at G and H. Prove that: (1) BGDH is a rectangle; (2) D is the midpoint of arc EF.

Home | Search | Geometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | Problems Art Gallery | Art | 981-990 | Arbelos | Semicircle | Perpendicular lines | Tangent Circles | Circle Tangent Line | Rectangle | Midpoint | Email | Solution / comment | by Antonio Gutierrez Last updated: Dec 27, 2014