Circumscribed Figure
A circumscribed figure is a polygon drawn outside a circle such that every side of the polygon touches the circle at exactly one point. In this geometric arrangement, all sides of the polygon act as tangents to the inscribed circle.
Key Concepts
Each side of a circumscribed polygon is a tangent to the inner circle, meeting it at a unique point of contact.
The center of the inscribed circle is equidistant from all sides of the circumscribed polygon.
When a quadrilateral circumscribes a circle, the sum of the lengths of its opposite sides is always equal due to the equal tangents theorem.
Formula & Equation
AB + CD = AD + BC
AB, BC, CD, and AD represent the lengths of the four sides of a quadrilateral ABCD that circumscribes a circle.
Common Misconceptions
Myth: A polygon is circumscribed around a circle as long as the circle is completely inside it.
Fact: Simply containing the circle is not enough. For a polygon to be circumscribed around a circle, every single side of the polygon must touch the circle at exactly one point, acting as a tangent.
Real World Applications
A square wooden frame built to tightly enclose a circular wall clock, where each inner edge of the frame touches the clock.
A triangular boundary wall constructed around a circular park such that the straight walls touch the circular path at three distinct points.
Frequently Asked Questions
What is a circumscribed quadrilateral?
It is a four-sided polygon drawn outside a circle such that all four of its sides touch the circle, acting as tangents.
What is the property of a quadrilateral circumscribing a circle?
For a circumscribed quadrilateral ABCD, the sum of the lengths of opposite sides is equal, meaning AB + CD = AD + BC.