If the distance from the center O to the chord AB is a, then the diameter of O is a

If the distance from the center O to the chord AB is a, then the diameter of O is a

AOB is isosceles right triangle, ab = 2A, OA = ob = √ 2a, diameter is 2 √ 2A

In a circle with a diameter of 3cm, the degree of the circumference angle of a 3 / 2cm chord is
It's better to have a picture of the process

If the diameter is 3, the radius is 3 / 2
If the chord is 3 / 2, the triangle formed by the chord and the radius at both ends is equilateral
So, the center angle of the chord is 60
The circle angle of the chord is 30

The radius of circle O is 4cm, the length of chord AB is 4cm, and the degree of the circular angle of chord AB is calculated

OA=OB=4,AB=4,
OA=OB=AB=4,
AOB is an equilateral triangle,
The center angle of the circle opposite to the chord AB = ∠ AOB = 60 °,
Circle angle of chord AB = center angle of chord AB / 2 = ∠ AOB / 2 = 30 °

If a chord is divided into two parts, one of which is four times as large as the other, the degree of the circumference angle of the chord is______ ．

As shown in the figure, AB divides the circle into two parts of 1:4, then ∠ AOB = 72 ° is known from the circle angle theorem, ∠ f = 12 ∠ AOB = 36 ° is known from the diagonal complementarity of the inscribed quadrilateral in the circle, ∠ e = 180 ° - ∠ f = 144 °. So the answer is 36 ° or 144 °