The diagonal of an isosceles trapezoid is perpendicular to the lateral side. Find the diagonal of the trapezoid if the radius

| April 11, 2021 | education

The diagonal of an isosceles trapezoid is perpendicular to the lateral side. Find the diagonal of the trapezoid if the radius of the circumscribed circle is 13cm, and the lateral side is 10cm.

By condition, the angle ACD of the trapezoid is 90. If the inscribed angle of the circle is 90, then it rests on the diameter of this circle. Then the base AD of the trapezoid is equal to the diameter of the circle.

AD = 2 * R = 2 * 13 = 26 cm.

Consider a right-angled triangle ACD, in which the side of the SD, according to the condition, is 10 cm, and the hypotenuse AD = 26 cm.

Then, by the Pythagorean theorem, the leg AC equal to the trapezoid diagonal will be equal to:

AC ^ 2 = AD ^ 2 – CD ^ 2 = 26 ^ 2 – 10 ^ 2 = 676 – 100 = 576.

AC = 24 cm.

Answer: The diagonal of the trapezoid is 24 cm.



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.