Known: as shown in the figure, take one side BC of triangle ABC as the diameter to make a semicircle, intersect AB at e, pass through e to make a semicircle, the tangent of O is just perpendicular to AC, try to determine the size relationship between BC and AC, and prove your conclusion The graph is a regular triangle, the upper corner is C, the left corner is B, the right corner is a, the tangent line is perpendicular to AC, and the intersection point is f

Known: as shown in the figure, take one side BC of triangle ABC as the diameter to make a semicircle, intersect AB at e, pass through e to make a semicircle, the tangent of O is just perpendicular to AC, try to determine the size relationship between BC and AC, and prove your conclusion The graph is a regular triangle, the upper corner is C, the left corner is B, the right corner is a, the tangent line is perpendicular to AC, and the intersection point is f

Proof: let the tangent here intersect with F, and let the center of the semicircle be o
EF is perpendicular to AC
OE is also perpendicular to AC (tangent)
Therefore, EF is parallel to OE
Because o is the midpoint of BC
So OE is the median line of triangle ABC
So OE = 1 / 2Ac
OE = 1 / 2BC (radius and diameter)
So there is BC = AC