As shown in the figure: in △ ABC, the semicircle o with ab as the diameter intersects AC BC at the point de. prove that the triangle ode is an equilateral triangle

As shown in the figure: in △ ABC, the semicircle o with ab as the diameter intersects AC BC at the point de. prove that the triangle ode is an equilateral triangle

O is the midpoint of ab. OA = ob = od = OE = R, so ∠ oad = ∠ ADO, ∠ OBE = ∠ BeO, and ∠ C = 60 °, so ∠ oad + ∠ OBE = 120 °, so ∠ ADO + ∠ BeO = 120 °, and ∠ bed + ∠ ade = 240 °, so ∠ OED + ∠ ode = 120 °
Because od = OE, so ∠ OED = ∠ ode = 60 °, so ∠ DOE = 60 °, so triangle ode is equilateral triangle

Elden Ring Premiere

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