Prove the calculation formula of sector area with radian system s = 0.5rl

Prove the calculation formula of sector area with radian system s = 0.5rl

Sector center angle θ radian
Sector area s = π R ^ 2*（ θ/ 2π)=0.5* θ* r^2
l=2πr*( θ/ 2π)= θ* r
S=0.5rl

In circle O, chord AB = 2 chord CD, what are the sizes of arc AB and arc CD >

It is known that the side opposite the 30 ° angle in a right triangle is half of the hypotenuse, so draw a right triangle in the circle, take the diameter of the circle as the hypotenuse (the circumferential angle opposite the diameter is 90 °), then the string AB in the question is the diameter, the string CD is the radius, take the endpoint of the diameter as the center of the circle, take the radius of circle O as the radius, and then draw a circle P and two circles

Would you please tell me the formula of the relationship between the string and the arc in the circle?

The chord length is a, the radius is r, and the center angle is α, Then cos α= 1-a^2/2R^2, α= arccos【1-a^2/2R^2】
Arc length = R * arccos [1-A ^ 2 / 2R ^ 2]

Known radius, chord length, vertical distance from chord to arc, unknown arc length 0

Just give the radius and chord length
Radius and chord length can know the angle
The sector area can be known by angle and radius
The area of the triangle can be known by the chord length and radius
The difference between the two is the area

In the circle, how to calculate the length of the string? I want the formula!

If the radius is r, the circumference is s = 2 π R. the angle corresponding to the chord is n. then l = N.2 π R / 360

Known AB、 CD is two arcs of the same circle, and AB=2 CD, the relationship between chord AB and 2CD is () A. AB=2CD B. AB＜2CD C. AB＞2CD D. Not sure

As shown in the figure, if the Arc de = arc CD is intercepted on the circle, there are: arc AB = arc CE
∴AB=CE
∵CD+DE=2CD＞CE=AB
∴AB＜2CD．
Therefore, B