Geometry Problem 1567: Finding Tangent Distances in a Circumscribed Isosceles Trapezoid. Academic Levels: Suitable for High School and College Mathematics Education

Given a circumscribed isosceles trapezoid ABCD about a circle with bases BC = 8 and AD = 12 units, determine the length of the segment joining the points of tangency on sides AB and CD.
 

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Key Definitions and Descriptions

Vocabulary	Description
Isosceles Trapezoid	A trapezoid with a pair of opposite sides that are equal in length.
Circumscribed	A figure that is drawn around another, touching it at points but not cutting it.
Tangential trapezoid, also called a Circumscribed Trapezoid	A trapezoid whose four sides are all tangent to a circle within the trapezoid
Circle	A round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).
Bases (BC and AD)	The two parallel sides of the trapezoid. Here, BC = 8 units and AD = 12 units.
Points of Tangency	The points where a circle touches a line or another circle.
Segment Joining Points of Tangency	The length of the segment connecting the points where the circle touches sides AB and CD of the trapezoid.

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