It is proved that even OD and BD are the midpoint of BC side because AB is the diameter ∴∠ ADB = ∠ BDC = 90 E.

∴DE=BE (the midline on the hypotenuse is equal to half of the hypotenuse) ∴∠EDB=∠EBD.

∴∠odb=∠obd ∴∠odb+∠edb=∠obd+∠ebd=90

∴DE is the tangent of the circle.