From the point O, which is the center of the circle, the perpendicular OM
| March 12, 2021 | education
From the point O, which is the center of the circle, the perpendicular OM is dropped onto the chord CE. Prove that point M is the midpoint of the chord.
Let us construct the radii OC and OE, and prove that the triangles COM and EOM are equal.
Triangles COM and EOM are rectangular since OM is perpendicular to CE, the leg OM is common for triangles, OC = OE = R. Then triangles COM and EOM are equal in leg and hypotenuse, and therefore CM = EM.
Then the point M is the midpoint of the chord CE, as required.
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