# Bellwork  If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number  Solve for x 21(x-4)=(2x-7)(x+2) 3x 2 -13x-7=0.

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Bellwork  If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number  Solve for x 21(x-4)=(2x-7)(x+2) 3x 2 -13x-7=0 Clickers

Bellwork Solutions  If 10 is multiplied by 10 more than a number, the product is the square of 24. Find the number

Bellwork Solutions  Solve for x 21(x-4)=(2x-7)(x+2) 3x 2 -13x-7=0

Section 10.6

The Concept  After discussing most of the angle relationships that we can find in a circle, today we’re going to move on to chord lengths  The concepts that drive our theorems today are based on the relationships we’ve already seen within a circle, but just need to be defined

Definition Segments of a chord The line segments formed when a chord is divided into two or more pieces Secant Segment Segment that contains a chord of a circle and has exactly one endpoint outside the circle. External Segment Exterior portion of secant segment A C B DEF G H

Theorem Theorem 10.14 If two chords intersect in the interior of a circle, then the product of the lengths of the segment of one chord is equal to the product of the lengths of the segments of the other chord. C B D A E

Example Solve for x A B C D E x+1 x+3 x+5 3

On your own  Solve for x x A C B D x+8 8 6

On your own  Solve for x x A C B D x+10 x 14

Theorem Theorem 10.15 If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment C B D A E

Example Solve for x A B C D E 3 x 5 4

On your own  Solve for x A C B E x 3 4 2

Theorems Theorem 10.16 If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment A B C D

Example Find the measure of angle AEC 8 16 x

On your own  What is the measure of angle ABC 15 14 x

Homework  10.6 1-22

Most Important Points  Segment Length formulas for inside a circle

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