Properties of Inscribed and Circumscribed Polygons

This video tutorial covers inscribed and circumscribed polygons, focusing on quadrilaterals. It explains the properties of inscribed quadrilaterals, such as supplementary opposite angles, and demonstrates how to calculate angles and arc measures. The tutorial also introduces circumscribed polygons, where all sides are tangent to a circle, and provides an example problem to calculate the perimeter of a circumscribed quadrilateral.

What is the definition of an inscribed polygon?

• A polygon with equal sides

• A polygon inside a square

• A polygon with all vertices on a circle

• A polygon with all sides tangent to a circle

If angle A of an inscribed quadrilateral is 70 degrees, what is the measure of its opposite angle C?

• 180 degrees

• 105 degrees

• 110 degrees

• 70 degrees

Given arc BC is 80 degrees and arc DC is 110 degrees, what is the measure of angle A in the inscribed quadrilateral?

• 105 degrees

• 95 degrees

• 115 degrees

• 85 degrees

What is the relationship between an inscribed angle and its intercepted arc?

• The inscribed angle is twice the intercepted arc

• The inscribed angle is half the intercepted arc

• The inscribed angle is one-third the intercepted arc

• The inscribed angle is equal to the intercepted arc

What is the measure of arc AD if the other arcs in the circle are 50, 80, and 110 degrees?

• 130 degrees

• 150 degrees

• 120 degrees

• 140 degrees

What defines a circumscribed polygon?

• A polygon with all vertices on a circle

• A polygon with all sides tangent to a circle

• A polygon inside another polygon

• A polygon with equal angles

If a polygon is circumscribed about a circle, what can we say about the circle?

• The circle is circumscribed about the polygon

• The circle is inscribed in the polygon

• The circle is outside the polygon

• The circle is tangent to the polygon

Given a circumscribed quadrilateral with sides AB = 14 and DC = 18, and a radius of 6, what is the length of side AD?

• 18

• 16

• 12

• 14

If the radius of the circumscribed circle is 6, what is the length of segment EH?

• 12

• 6

• 24

• 18

What is the perimeter of a circumscribed quadrilateral with sides 14, 12, 18, and 20?

• 68

• 72

• 64

• 60