The diameter CD of the circle is perpendicular to the chord AB. It is known that the angle CDA = 20 °.

| September 21, 2021 | education

The diameter CD of the circle is perpendicular to the chord AB. It is known that the angle CDA = 20 °. Calculate the degree measures of the angles of the triangle ACB.

The AOD triangle is rectangular, since AB is perpendicular to CD by condition, and the angle ODA = CDA = 20. Then the angle OAD = 180 – 90 – 20 = 70.

Consider a triangle ACD, which is inscribed in a circle, and its side is equal to the diameter, therefore, the angle CAD is a straight line, since from is based on the diameter. Then the angle CAO = 90 – OAD = 90 – 70 = 20.

Then in a right-angled triangle AOC, the angle AOC = 90 – 20 = 70.

Rectangular triangles AOC and BOC are equal, since the leg CO is common 1, and the legs AO = BO, since the diameter is perpendicular to the chord and divides it in half. Then the angle СAO = СBО = 20, and the angle АСB = 2 * АСО = 2 * 70 = 140.

Answer: The angles of the ABC triangle are 20, 20, 140.



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.