# A trapezoid is inscribed in a circle of radius 29, the bases of which are 40

September 30, 2021 | education

| **A trapezoid is inscribed in a circle of radius 29, the bases of which are 40 and 42, and the center of the circle lies outside the trapezoid. Find the height of this trapezoid.**

In a right-angled triangle OHD, according to the Pythagorean theorem, we determine the length of the leg OH.

OH ^ 2 = OD ^ 2 – D ^ 2 = 841 – 441 = 400.

OH = 20 cm.

In a right-angled triangle OCK, by the Pythagorean theorem, we determine the length of the leg OC.

OK ^ 2 = OC ^ 2 – CK ^ 2 = 841 – 400 = 441.

OK = 21 cm.

Then HC = OK – OH = 21 – 20 = 1 cm.

Answer: The height of the trapezoid is 1 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.