Homework Solutions

Geometry CP, May 3

Circles: Inscribed Angles and Tangents

Book Section: 10-4 & 10-5

Essential Question: What are inscribed angles in circles, circle tangents

and how can they be used?

Standards: G-5.1, .4, .5; CCSS C.GMD.1, .3; G-C.2, .5

Definitions

• Inscribed angle – an angle that has a vertex on the

circle and sides that are chords of the circle.

• Intercepted arc – an arc with endpoints on the side of an

inscribed angle and lies in the interior of the inscribed

angle.

How?

Inscribed Angle Theorem

Example 1 Use Inscribed Angles to Find Measures

A. Find mX.

Example 1 Use Inscribed Angles to Find Measures

B.

In a World of Equals

Example 2 Use Inscribed Angles to Find Measures

ALGEBRA Find mR.

Triangles – In a Circular World

Example 4 Find Angle Measures in Inscribed Triangles

ALGEBRA Find mB.

Quadrilaterals, Too?

Example 5 Find Angle Measures

INSIGNIAS An insignia is an emblem that signifies rank, achievement, membership, and so on. The insignia shown is a quadrilateral inscribed in a circle. Find mS and mT.

More Definitions

• Tangent – a line in the same plane as a circle that

intersects the circle at exactly one point, called the

point of tangency.

• Common tangent – a line, ray, or segment that is

tangent to two circles.

Some Tangent Theory

Example 6 Identify a Tangent

More Equality (or Congruence)

Example 7 Use Congruent Tangents to Find Measures

One More Definition

• Circumscribed polygon – a polygon is circumscribed

about a circle if every side of the polygon is tangent to

the circle.

Example 8 Find Measures in Circumscribed

Polygons

Examples

Classwork: Textbook p.727, 2-12 even;

p.736, 4-16 even

Homework: HW Due 5/7, All (both sides)