Proof: if there is a circle whose any two strings are equal, then the arcs of the two strings are equal

Connect OA, ob, OC, OD
Chord AB = CD in circle O
OA=OC
OB=OD
Triangle OAB is equal to triangle OCD
Angle AOB = angle cod
Arc AB = arc CD

It is proved that the arcs between two parallel strings of a circle are equal
Write down the general process and known
Urgent //
We haven't learned the central angle yet
out-of-service

The diameter perpendicular to the chord bisects the chord, and bisects the two arcs corresponding to the chord. (theorem) this theorem should be learned? 1. Any diameter will divide the circle into two arcs of equal length. 2. (theorem) = > the diameter perpendicular to the chord bisects the two arcs corresponding to two parallel strings respectively. 1 & 2 = > "two strings bisected by diameter"

In the same circle or the same circle, the same arc or the same arc opposite the circle angle is equal. I don't think the premise of "in the same circle or the same circle" is necessary, because the same arc is the arc that can be completely coincident, so as long as it is the same arc, it must be in the same circle or the same circle, However, the definition in the book has the premise of "in the same circle or in the same circle". Please give a reply. Note that equal arcs are arcs with equal radians and length, that is, arcs that can be completely coincident```
In plane geometry, it is stipulated that "in the same circle or equal circle, the arcs that can completely coincide are called equal arcs."

Support your opinion. Some statements in the textbook are not absolute. There are some different contents in each textbook adaptation, which means that not all the contents in the textbook itself are accurate. You have a spirit of independent thinking, which is a valuable part of a student. If you carry it forward, it will be of great benefit to your future study and work

How to prove that in the same circle or equal circle, the same arc or equal arc is equal to the circumference angle

We prove that: (1) if the edge ab of the circular angle ABC passes through the origin o, then in △ AOC, Ao = co --- > angle a = angle OCA, the center angle OBC is the outer angle of △ AOC, so the angle BOC = 2-angle OAC, so the angle OAC = (1 / 2) angle BOC. So the circular angle BAC = half of the center angle BOC. (2) if the center O is inside △ ABC, the diameter ad "..."

1. In the same circle, the circle angles of the same chord are equal, and the circle angles of the second-order arc are equal. Which pair of these two is right? Why

The second is right
A string can correspond to two circular angles, which complement each other, so 1 is incorrect

In the same circle and the same circle, the arc of the equal circle angle is equal? What if it is a chord?

The arc length is the angle multiplied by the radius, so both are equal. The chord length is the sine half of the angle multiplied by the radius, and then multiplied by two, so they are also equal!
There is a simpler way: the same circle or the same circle can be drawn to coincide, and the same circle angle can be drawn to coincide, so the opposite arc or string will also coincide. Do you think they are not equal?

It is known that the two different intersections of the parabola y = AX2 + 2x + C and X-axis are on the right side of the origin, then the point m (a, c) is on the second side___ &Quadrant

When a ＞ 0, △ 4-4ac ＞ 0f (0) = C ＞ 0-22a ＞ 0, there is no solution; when a ＜ 0, △ 4-4ac ＞ 0f (0) = C ＜ 0-22a ＞ 0, then a ＜ 0, C ＜ 0; then point (a, c) is in the third quadrant

It is known that if the intersection points of the parabola y = ax + BX + C and X axis are on the right side of the origin, then the point m (a, c) is in the quadrant

First and fourth

Given that the parabola y = (k-1) x ^ + 2x + 2k-k ^ passes through the origin and the opening is downward, the analytic expression of the quadratic function corresponding to the parabola is obtained

The parabola passes through the origin,
By substituting the origin coordinates (0,0) into the analytical formula, we get the following result:
2k－k²=0,
Ψ k = 0 or K = 2,
And he opened his mouth down,
∴﹙k－1﹚＜0,
∴k＜1,
∴k=0,
The analytical formula of parabola is y = - X & # 178; + 2x

When k is a negative integer, the intersection point of quadratic function y = x & # 178; - (1 + 2K) x + K & # 178; - 2 and X axis is an integer point, and the analytical formula of parabola is obtained

y=x²-(1+2k)x+k²-2
Let y = 0 be X & # 178; - (1 + 2K) x + K & # 178; - 2 = 0
Δ=（1+2k)²-4(k²-2)=9+4k≥0
∴ k≥-9/4
∵ K is a negative integer
∴k=-2,-1
The intersection of quadratic function and X axis is an integer point
Ψ Δ = 9 + 4K is a square number
When k = - 1, Δ = 5 has no meaning
When k = - 2, Δ = 1
In this case, the quadratic equation is X & # 178; + 3x = 0
The solution is x = 0 or x = - 1
The analytic formula of parabola is y = x & # 178; + 3x

Proof: if there is a circle whose any two strings are equal, then the arcs of the two strings are equal