Lesson 7 - Proportions Involving Segments of Chords Tangents and Secants

Chords and intersect inside a circle at E.

If , , and , then .

Chords and intersect inside a circle at E.

If , , and , then

Chords and intersect inside a circle at X.

If , , and X is the midpoint of , then

Secants and are drawn to a circle from P.

a) If , , and , then .

Secants and are drawn to a circle from P.

a) If , , and , then .

Secants and are drawn to a circle from P.

a) If , , and , then

Secants and are drawn to a circle from P.

a) If , , and , then .

A tangent and a secant are drawn to the same circle from Point P. The

external segment of the secant is 4 and the length of the tangent is 6. The length

of the secant is

A tangent and secant are drawn to the same circle from Point P. If

and , then .

A tangent and a secant are drawn to the same circle from point P. The

internal segment of the secant is 8 and its external segment is 4. The length of

the tangent is .

*Keep answer in simplest radical form.

In the diagram below, is circumscribed about circle O and the sides of are tangent to the circle at points D, E, and F.

If , , and , then .

In the diagram below, , , and are tangents to circle O at points F, E, and D, respectively, , , and .

Perimeter of

In the accompanying diagram of a circle, chords and intersect at E, and .

In circle O attached, diameter is perpendicular to chord at E. If , , and , what is the length of .

In the accompanying diagram of circle O, chords and intersect at E. If , , and , then .

In circle O, diameter is perpendicular to chord at E. If and , then .

In the diagram below of circle O, secant intersects circle O at D, secant intersects circle O at E, , and .

Find:

In the accompanying diagram, is tangent to circle O at A, is a secant, , and .

*Keep in simplest radical form.

In the diagram below, circle O has a radius of 5, and . Diameter is perpendicular to chord at E.

In circle O below, secants and are drawn from external Point P.

If and , then .

*Round answer to nearest tenth.

In the accompanying diagram, tangent and secant are drawn to circle O from point A, if and , then .

In the attached figure, quadrilateral TAEO is circumscribed around circle D. The midpoint of is R, and . If and , what is the perimeter of quadrilateral TAEO?

Perimeter of

Circle O is drawn below with secant . The length of tangent is 24.

If the ratio of is , then .

In the accompanying diagram, , , and are tangent to circle O at F, E, and G, respectively. If , and , then .

In the diagram below, secants and are drawn to a circle from Point P.

If and , then .

In the diagram shown below, is tangent to circle T at A, and secant is drawn where point B is on circle T.

If and , then .

*Keep answer in simplest radical form