A circle inscribed in an isosceles trapezoid divides the lateral side by the point of contact

| May 1, 2021 | education

A circle inscribed in an isosceles trapezoid divides the lateral side by the point of contact into 8cm and 18cm long segments. Find the bases of the trapezoid and the radius of the inscribed circle.

Let’s construct the radii of the circle OK, OH, OP, OM to the points of tangency of the trapezoid and the circle.

By the property of tangents drawn from one point, DM = DH = 18 cm, AM = AK = 18 cm.

BP = BK = 8 cm, CP = CH = 8 cm.

Then AD = AM + DK = 18 + 18 = 36 cm, BC = BP + CP = 8 + 8 = 16 cm.

Since a circle is inscribed in the trapezoid, its radius is the average proportional to the segments into which the circle divides the lateral side.

R = OH = √CH * DH = √8 * 18 = √144 = 12 cm.

Answer: The bases of the trapezoid are 16 cm, 32 cm, the radius of the circle is 12 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.