Geometry Chapter 10 10 6 FIND SEGMENT LENGTHS

Geometry Chapter 10 10 -6: FIND SEGMENT LENGTHS IN CIRCLES

Warm-Up

Warm-Up

Warm-Up

Warm-Up

Warm-Up

Warm-Up

Warm-Up

Warm-Up

Warm-Up

Find Segment Lengths in Circles Objective: Students will be able to find segment lengths of chords, secants, and tangents of circles. Agenda Chord Lengths Secant Lengths Tangent Lengths

Segments of Chords When two chords intersect in the interior of a circle, each chord is divided into two segments that are called segments of the chord. D A E C B

Theorem 10. 14 – Segments of Chords Theorem: If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. D A E C B

Example 1

Example 1

Example 1

Example 1

Example 1

Example 2

Example 2

Example 2

Example 2

Tangents and Secants A secant segment is a segment that contains a chord of the circle, and has exactly one endpoint outside the circle. The part of the secant segment that is outside the circle is called the external segment. B C A D

Theorem 10. 15 – Segments of Secants Theorem: If two secant segments share the same endpoint, then the product of the lengths of each secant segment, along with its external segment, are equal. B A E C D

Example 3 a Find the value(s)of x.

Example 3 a Find the value(s)of x.

Example 3 a Find the value(s)of x.

Example 3 a Find the value(s)of x.

Example 3 b Find the value(s)of x.

Example 3 b Find the value(s)of x.

Example 3 b Find the value(s)of x.

Example 3 c Find the value(s)of x.

Example 3 c Find the value(s)of x.

Example 3 c Find the value(s)of x.

Example 3 c Find the value(s)of x.

Example 3 c Find the value(s)of x. Why?

Theorem 10. 16 – Segments of Secants and Tangents Theorem: If a secant and a tangent segment share the same endpoint, then the product of the lengths of the secant segment and its external segment equal the square of the length of the tangent segment. A E C D

Example 4 Find the value of x.

Example 4 Find the value of x.

Example 4 Find the value of x.

Example 4 Find the value of x.

Example 5 Find the value of x.

Example 5 Find the value of x.

Example 5 Find the value of x.

Extra Practice Find the value of x. State which theorem you used. 1. ) 2. )

Extra Practice Find the value of x. State which theorem you used. 3. ) 4. )

Extra Practice 1. ) Find the value of x. State which theorem you used.

Extra Practice 1. ) Find the value of x. State which theorem you used.

Extra Practice 2. ) Find the value of x. State which theorem you used.

Extra Practice 2. ) Find the value of x. State which theorem you used.

Extra Practice 3. ) Find the value of x. State which theorem you used.

Extra Practice 3. ) Find the value of x. State which theorem you used.

Extra Practice 4. ) Find the value of x. State which theorem you used.

Extra Practice 4. ) Find the value of x. State which theorem you used.