A circle is inscribed in the trapezoid. Find the radius of the circle if the lateral side is divided by the point

| June 14, 2021 | education

A circle is inscribed in the trapezoid. Find the radius of the circle if the lateral side is divided by the point of tangency into segments a, b.

Let’s connect point O, the center of the circle, with points A and B on the side of the trapezoid. By the property of the trapezoid into which the circle is inscribed, the triangle AOB is rectangular with a right angle at the point O.

From point O we draw the radius OH to the point of tangency of the circle with the lateral side AB. By the property of a tangent, the radius of a circle drawn to the tangent point is perpendicular to the tangent. Then in a right-angled triangle ABO, segment OH, there is a height drawn from a right angle to the hypotenuse, which means OA ^ 2 = AH * BH = a * b.

ОА = √ (a * b) see.

Answer: The radius of the circle is √ (a * b) 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.