Through point A of the circle, chords of length AC = 2r, AB = r, AD = r are drawn, where r is the radius of the circle

| July 6, 2021 | education

Through point A of the circle, chords of length AC = 2r, AB = r, AD = r are drawn, where r is the radius of the circle. Find the angles of the quadrilateral ABCD and the degree micrometers of the arcs AB, DC, CD, AD

Since the arc AC = 2 * r, it coincides with the diameter of the circle.

Then the triangles ABC and ADC are rectangular, since the coal B and D are based on the diameter of the circle.

The segment AB of the triangle ABC is equal to half of the hypotenuse AC, then the angle ACB = 30, and the angle ACB = 180 – 90 – 30 = 60.

The ABC triangle is equal to the ACD triangle along the leg and the hypotenuse – the fourth sign of equality, then the angle BAD = 2 * BAC = 2 * 60 = 100, angle BCD = 2 * ACB = 2 * 30 = 60, angles ABC and ADC = 90.

Arc AB is equal to arc AD and is equal to 2 * 30 = 60.

Arc CD = 2 * DBC = 2 * 60 = 120.

Arc DСВ = 2 * 120 = 240.

Answer: The angles of the quadrangle ABCD are equal to 60, 90, 120, 90, arc AD = 60, AB = 60, CD = 120, DCB = 240.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.