   Chapter 6.3, Problem 35E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given: Tangents A B ¯ , B C ¯ ,     and     A C ¯     t o     ⊙ O at points M, N, and P, respectively. A B = 14 , B C = 16 , A C = 12 Find: AM, PC, and BN To determine

To find:

To find AM, PC, and BN.

Explanation

Given that, Tangents AB¯,BC¯, and AC¯ to O at points M, N, and P, respectively AB=14,BC=16,AC=12

The tangents segments from an external point are congruent. Therefore,

AM=AP=xBM=BN=yCN=CP=z

The diagrammatic representation is given below,

We know that,

AB=AM+MB=x+yBC=BN+NC=y+zAC=AP+PC=x+z

Substitute the value of AB=14,BC=16,AC=12 in the above equation to get the following,

x+y=14...(1)y+z=16...(2)x+z=12...(3)

Solve equation (1) and (2) to get the following,

x+y+0z=140x+y+z=16()(

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