Inscribed Shapes: Problem Solving

Explanation

An inscribed shape is a polygon whose vertices all lie on a circle. Common inscribed shapes include triangles, quadrilaterals, and regular polygons.

Key ideas:

• Inscribed angles intercept arcs of the circle.

• In an inscribed triangle, the sum of interior angles is still 180°.

• A quadrilateral inscribed in a circle is called a cyclic quadrilateral.

• Opposite angles in a cyclic quadrilateral add up to 180°.

Problem solving often involves:

• Using arc measures to find angles

• Using angle relationships to find missing values

Quiz (5 Questions)

1. What does it mean for a shape to be inscribed in a circle?

2. An inscribed angle intercepts a 100° arc. What is the angle measure?

3. If one angle of a cyclic quadrilateral is 70°, what is the opposite angle?

4. True or False: All quadrilaterals can be inscribed in a circle.

5. A triangle is inscribed in a circle. One angle intercepts a semicircle. What is the angle?

Answer Key

1. All vertices lie on the circle

2. 50°

3. 110°

4. False

5. 90°