As shown in the figure, AB and CD are the two chords of circle O. points E and F are the midpoint of AB and CD, connecting EF, angle AEF = angle CFE, and proving AB = CD

As shown in the figure, AB and CD are the two chords of circle O. points E and F are the midpoint of AB and CD, connecting EF, angle AEF = angle CFE, and proving AB = CD

Connect OE, of,
∵ E and F are the middle points of the strings AB and CD respectively
⊥ OE ⊥ AB, of ⊥ CD, (vertical diameter theorem)
∵∠AEF=∠CFE,
∴∠OEF=∠OFE,
∴OE=OF,
х AB = CD (the pairs in the hearts of equal strings are equal)

AC and BD are chords of ⊙ o, and AC ┻ BD point P, OM ┻ AB are at point m, and N is the midpoint of CD. It is proved that OM is equal to PN

Make diameter AE, connect EB and EC
Then OM is the median line of △ Abe
∴OM＝1/2BE
∵ AE is the diameter
∴∠ACE＝90°
That is AC ⊥ CE
∵AC⊥BD
∴BD‖CE
‖ arc CD = arc be
∴CD＝BE
∴OM＝1/2BE
∵ n is the midpoint of RT △ PCD hypotenuse CD
∴PN＝1/2CD
∴OM＝PN

What is the plane angle of dihedral angle? How to find it?

Dihedral angle refers to the angle between two planes. When calculating, it is required to find out the vertical line perpendicular to the intersection line of two planes. The angle formed by these two vertical lines is dihedral angle. If two vertical lines intersect at a point, then a plane angle is formed, which is called the plane angle of dihedral angle