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Laabri

Lesson 7 - Proportions Involving Segments of Chords Tangents and Secants

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Last updated about 1 month ago
27 Nsɛmmisa
Proportional Parts of Intersecting Chords
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Secant-Secant Proportional Parts
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Tangent - Secant
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Tangent Tangent
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More Shots
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Textbooky Notes

Intersecting Chords - Proportional Parts

GeoGebra Investigation

Asemmisa {{asɛmmisaAhyɛnsode}}
1.

Chords

and
intersect inside a circle at E.

If

,
, and
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
2.

Chords

and
intersect inside a circle at E.

If

,
, and
, then

Asemmisa {{asɛmmisaAhyɛnsode}}
3.

Chords

and
intersect inside a circle at X.

If

,
, and X is the midpoint of
, then

Textbooky Notes

Secant Secant - Proportional Parts

GeoGebra Investigation

Asemmisa {{asɛmmisaAhyɛnsode}}
4.

Secants

and
are drawn to a circle from P.

a) If

,
, and
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
5.

Secants

and
are drawn to a circle from P.

a) If

,
, and
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
6.

Secants

and
are drawn to a circle from P.

a) If

,
, and
, then

Asemmisa {{asɛmmisaAhyɛnsode}}
7.

Secants

and
are drawn to a circle from P.

a) If

,
, and
, then
.

Textbooky Notes

Tangent - Secant - Proportional Parts

GeoGebra Investigation

Asemmisa {{asɛmmisaAhyɛnsode}}
8.

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

Asemmisa {{asɛmmisaAhyɛnsode}}
9.

A tangent

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

and
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
10.

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.

Asemmisa {{asɛmmisaAhyɛnsode}}
11.

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
.

Asemmisa {{asɛmmisaAhyɛnsode}}
12.

In the diagram below,

,
, and
are tangents to circle O at points F, E, and D, respectively,
,
, and
.

Perimeter of

Asemmisa {{asɛmmisaAhyɛnsode}}
13.

In the accompanying diagram of a circle, chords

and
intersect at E,
and
.

Asemmisa {{asɛmmisaAhyɛnsode}}
14.

In the circle below, secants

and
intersect at T,
, and
.

Which equation could be used to find the value of x?

Asemmisa {{asɛmmisaAhyɛnsode}}
15.

In circle O attached, diameter

is perpendicular to chord
at E. If
,
, and
, what is the length of
.

Asemmisa {{asɛmmisaAhyɛnsode}}
16.

In the accompanying diagram of circle O, chords

and
intersect at E. If
,
, and
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
17.

In circle O, diameter

is perpendicular to chord
at E. If
and
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
18.

In the diagram below of circle O, secant

intersects circle O at D, secant
intersects circle O at E,
, and
.

Find:

Asemmisa {{asɛmmisaAhyɛnsode}}
19.

In the accompanying diagram,

is tangent to circle O at A,
is a secant,
, and
.

*Keep in simplest radical form.

Asemmisa {{asɛmmisaAhyɛnsode}}
20.

In the diagram below, circle O has a radius of 5, and

. Diameter
is perpendicular to chord
at E.

Asemmisa {{asɛmmisaAhyɛnsode}}
21.

In circle O below, secants

and
are drawn from external Point P.

If

and
, then
.

*Round answer to nearest tenth.

Asemmisa {{asɛmmisaAhyɛnsode}}
22.

In the accompanying diagram, tangent

and secant
are drawn to circle O from point A, if
and
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
23.

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

Asemmisa {{asɛmmisaAhyɛnsode}}
24.

Circle O is drawn below with secant

. The length of tangent
is 24.

If the ratio of

is
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
25.

In the accompanying diagram,

,
, and
are tangent to circle O at F, E, and G, respectively. If
, and
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
26.

In the diagram below, secants

and
are drawn to a circle from Point P.

If

and
, then
.

Asemmisa {{asɛmmisaAhyɛnsode}}
27.

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