Tangent and a Chord

R10

DiameterSemicircleRadius

ChordTangentSecant

Central AngleInscribed AngleMajor ArcMinor Arc

Angle Rules

Central

Rule:______

Inscribed

Rule:______

Tangent and a Chord

Rule:______

Arcs and Parallel ChordsIntersecting Chords

Rule:______Rule:______

Tangents and Secants

Rule:______

A Tangent anda Secant Two Tangents Two Secants

1.In the diagram below, trapezoid ABCD, with bases and , is inscribed in circle O, with diameter . If , find .

2.In the diagram below of circle O, chords and intersect at E, , and .What is the degree measure of ?

3.In the diagram below of circle O, chords and intersect at point B, such that and . What is ?

4.In the diagram below, tangent and secant are drawn to circle O. The ratio is . Find .

5.In the diagram of circle O below, chords and are parallel, and is a diameter of the circle.If , what is ?

6.In the diagram below, two parallel lines intersect circle O at points A, B, C, and D, with and . Find .

Length Rules

Intersecting Chords

Rule:______

Common Tangents

Rule:______

Lengths of Tangents and Secants

Two Secants Tangent and a Secant

Rule:______Rule:______

1.In the diagram of circle O below, chord intersects chord at E, , , , and . What is the value of x?

2.In the diagram below of circle O, diameter is perpendicular to chord at E. If and , find the length of .

3.In the diagram below of circle O, chord bisects chord at E. If and , find the length of in simplest radical form.

4.In the diagram below of circle O, radius is 5 cm. Chord is 8 cm and is perpendicular to at point P.What is the length of , in centimeters?

5.How many common tangent lines can be drawn to the two externally tangent circles shown below?

6.In the diagram below, , , and are tangents to circle O at points F, E, and D, respectively, , , and . What is the perimeter of ?

7.In the diagram below, circles X and Y have two tangents drawn to them from external point T. The points of tangency are C, A, S, and E. The ratio ofTA to AC is 1:3. If TS = 24, find the length of SE.

8.In the diagram below,tangent and secant are drawn to circle O from external point P. If and , what is the length of ?

9.In the diagram below of circle O, chords and intersect at M. Secant and tangent are drawn to circle O. The length of is two more than the length of , , , and . Find the length of . Find the length of .

10.In the diagram below of circle O, secant intersects circle O at D, secant intersects circle O at E, , , and . What is the length of ?

Equations of Circles

Center at the origin (0,0) Center at the point (h, k)

withradius r units. withradius r units.

______

1.What are the center and the radius of the circle whose equation is ?

2.Write an equation for each circle whose center is (-3, 2) and whose diameter is 10.

3.Write an equation represents the circle whose center is and whose radius is 5?

4.A circle is represented by the equation . What are the coordinates of the center of the circle and the length of the radius?

5.Write an equation for the circle shown in the graph below?

6.Write the equation represents circle K shown in the graph below?

7.Write an equation of the circle graphed in the diagram below.

8.What is an equation of a circle with its center at and a radius of 4?