# 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.

A circle within,
Tangents touch trapezoid's sides,
Solve the distance now.

## 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.