Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Chapter 10.7, Problem 20PSB
To determine

Find the perimeter of ABCD.

Expert Solution & Answer
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Answer to Problem 20PSB

  6+63

Explanation of Solution

Given information:

ABCD is a kite, with AB¯BC¯ , AD¯CD¯ , and mB=120 . The radius of the circle is 3.

  Geometry For Enjoyment And Challenge, Chapter 10.7, Problem 20PSB , additional homework tip  1

Calculation:

Consider the given figure,

  Geometry For Enjoyment And Challenge, Chapter 10.7, Problem 20PSB , additional homework tip  2

  AB¯BC¯ , AD¯CD¯ , mB=120 (given)

Two congruent chords correspond congruent arc,

  mAB=mBC,mAD=mCD

The measure of the angle with vertex on the circle is half the measure of the intercepted arc,

  mABC=120°=mAD+mCD2=2mAD2mAD=mCD=120°mAB+mBC+mAD+mCD=360°putvalues(2)120°+2mAB=360°2mAB=360°240°2mAB=120°mAB=60°

Now again the measure of the angle with vertex on the circle is half the measure of the intercepted arc,

  mADB=mAB2=60°2=30°mBAD=mBC+mCD2=60°+120°2=90°BD=6AB=BC2=62=3AB2+AD2=BD232+AD2=62AD2=369=27AD=332AB+2AD=6+2.33=6+63Perimeter=6+63

Hence, the perimeter of ABCD is 6+63

Chapter 10 Solutions

Geometry For Enjoyment And Challenge

Ch. 10.1 - Prob. 11PSBCh. 10.1 - Prob. 12PSBCh. 10.1 - Prob. 13PSBCh. 10.1 - Prob. 14PSBCh. 10.1 - Prob. 15PSBCh. 10.1 - Prob. 16PSBCh. 10.1 - Prob. 17PSBCh. 10.1 - Prob. 18PSBCh. 10.1 - Prob. 19PSCCh. 10.1 - Prob. 20PSCCh. 10.1 - Prob. 21PSCCh. 10.1 - Prob. 22PSCCh. 10.1 - Prob. 23PSCCh. 10.1 - Prob. 24PSCCh. 10.1 - Prob. 25PSCCh. 10.2 - Prob. 1PSACh. 10.2 - Prob. 2PSACh. 10.2 - Prob. 3PSACh. 10.2 - Prob. 4PSACh. 10.2 - Prob. 5PSACh. 10.2 - Prob. 6PSACh. 10.2 - Prob. 7PSBCh. 10.2 - Prob. 8PSBCh. 10.2 - Prob. 9PSBCh. 10.2 - Prob. 10PSBCh. 10.2 - Prob. 11PSBCh. 10.2 - Prob. 12PSBCh. 10.2 - Prob. 13PSBCh. 10.2 - Prob. 14PSCCh. 10.2 - Prob. 15PSCCh. 10.2 - Prob. 16PSCCh. 10.3 - Prob. 1PSACh. 10.3 - Prob. 2PSACh. 10.3 - Prob. 3PSACh. 10.3 - Prob. 4PSACh. 10.3 - Prob. 5PSACh. 10.3 - Prob. 6PSACh. 10.3 - Prob. 7PSACh. 10.3 - Prob. 8PSACh. 10.3 - Prob. 9PSACh. 10.3 - Prob. 10PSACh. 10.3 - Prob. 11PSBCh. 10.3 - Prob. 12PSBCh. 10.3 - Prob. 13PSBCh. 10.3 - Prob. 14PSBCh. 10.3 - Prob. 15PSBCh. 10.3 - Prob. 16PSBCh. 10.3 - Prob. 17PSBCh. 10.3 - Prob. 18PSBCh. 10.3 - Prob. 19PSBCh. 10.3 - Prob. 20PSBCh. 10.3 - Prob. 21PSCCh. 10.3 - Prob. 22PSCCh. 10.4 - Prob. 1PSACh. 10.4 - Prob. 2PSACh. 10.4 - Prob. 3PSACh. 10.4 - Prob. 4PSACh. 10.4 - Prob. 5PSACh. 10.4 - Prob. 6PSACh. 10.4 - Prob. 7PSACh. 10.4 - Prob. 8PSACh. 10.4 - Prob. 9PSACh. 10.4 - Prob. 10PSBCh. 10.4 - Prob. 11PSBCh. 10.4 - Prob. 12PSBCh. 10.4 - Prob. 13PSBCh. 10.4 - Prob. 14PSBCh. 10.4 - Prob. 15PSBCh. 10.4 - Prob. 16PSBCh. 10.4 - Prob. 17PSBCh. 10.4 - Prob. 18PSBCh. 10.4 - Prob. 19PSBCh. 10.4 - Prob. 20PSBCh. 10.4 - Prob. 21PSCCh. 10.4 - Prob. 22PSCCh. 10.4 - Prob. 23PSCCh. 10.4 - Prob. 24PSCCh. 10.4 - Prob. 25PSCCh. 10.4 - Prob. 26PSCCh. 10.4 - Prob. 27PSCCh. 10.4 - Prob. 28PSCCh. 10.4 - Prob. 29PSCCh. 10.5 - Prob. 1PSACh. 10.5 - Prob. 2PSACh. 10.5 - Prob. 3PSACh. 10.5 - Prob. 4PSACh. 10.5 - Prob. 5PSACh. 10.5 - Prob. 6PSACh. 10.5 - Prob. 7PSACh. 10.5 - Prob. 8PSACh. 10.5 - Prob. 9PSACh. 10.5 - Prob. 10PSACh. 10.5 - Prob. 11PSACh. 10.5 - Prob. 12PSACh. 10.5 - Prob. 13PSACh. 10.5 - Prob. 14PSACh. 10.5 - Prob. 15PSACh. 10.5 - Prob. 16PSACh. 10.5 - Prob. 17PSACh. 10.5 - Prob. 18PSBCh. 10.5 - Prob. 19PSBCh. 10.5 - Prob. 20PSBCh. 10.5 - Prob. 21PSBCh. 10.5 - Prob. 22PSBCh. 10.5 - Prob. 23PSBCh. 10.5 - Prob. 24PSBCh. 10.5 - Prob. 25PSBCh. 10.5 - Prob. 26PSBCh. 10.5 - Prob. 27PSBCh. 10.5 - Prob. 28PSBCh. 10.5 - Prob. 29PSBCh. 10.5 - Prob. 30PSBCh. 10.5 - Prob. 31PSCCh. 10.5 - Prob. 32PSCCh. 10.5 - Prob. 33PSCCh. 10.5 - Prob. 34PSCCh. 10.5 - Prob. 35PSCCh. 10.5 - Prob. 36PSCCh. 10.6 - Prob. 1PSACh. 10.6 - Prob. 2PSACh. 10.6 - Prob. 3PSACh. 10.6 - Prob. 4PSACh. 10.6 - Prob. 5PSACh. 10.6 - Prob. 6PSACh. 10.6 - Prob. 7PSACh. 10.6 - Prob. 8PSACh. 10.6 - Prob. 9PSACh. 10.6 - Prob. 10PSACh. 10.6 - Prob. 11PSACh. 10.6 - Prob. 12PSACh. 10.6 - Prob. 13PSBCh. 10.6 - Prob. 14PSBCh. 10.6 - Prob. 15PSBCh. 10.6 - Prob. 16PSBCh. 10.6 - Prob. 17PSBCh. 10.6 - Prob. 18PSBCh. 10.6 - Prob. 19PSBCh. 10.6 - Prob. 20PSBCh. 10.6 - Prob. 21PSBCh. 10.6 - Prob. 22PSCCh. 10.6 - Prob. 23PSCCh. 10.6 - Prob. 24PSCCh. 10.6 - Prob. 25PSCCh. 10.6 - Prob. 26PSCCh. 10.6 - Prob. 27PSCCh. 10.6 - Prob. 28PSCCh. 10.7 - Prob. 1PSACh. 10.7 - Prob. 2PSACh. 10.7 - Prob. 3PSACh. 10.7 - Prob. 4PSACh. 10.7 - Prob. 5PSACh. 10.7 - Prob. 6PSACh. 10.7 - Prob. 7PSACh. 10.7 - Prob. 8PSACh. 10.7 - Prob. 9PSBCh. 10.7 - Prob. 10PSBCh. 10.7 - Prob. 11PSBCh. 10.7 - Prob. 12PSBCh. 10.7 - Prob. 13PSBCh. 10.7 - Prob. 14PSBCh. 10.7 - Prob. 15PSBCh. 10.7 - Prob. 16PSBCh. 10.7 - Prob. 17PSBCh. 10.7 - Prob. 18PSBCh. 10.7 - Prob. 19PSBCh. 10.7 - Prob. 20PSBCh. 10.7 - Prob. 21PSCCh. 10.7 - Prob. 22PSCCh. 10.7 - Prob. 23PSCCh. 10.7 - Prob. 24PSCCh. 10.7 - Prob. 25PSCCh. 10.7 - Prob. 26PSCCh. 10.7 - Prob. 27PSCCh. 10.8 - Prob. 1PSACh. 10.8 - Prob. 2PSACh. 10.8 - Prob. 3PSACh. 10.8 - Prob. 4PSACh. 10.8 - Prob. 5PSACh. 10.8 - Prob. 6PSACh. 10.8 - Prob. 7PSACh. 10.8 - Prob. 8PSBCh. 10.8 - Prob. 9PSBCh. 10.8 - Prob. 10PSBCh. 10.8 - Prob. 11PSBCh. 10.8 - Prob. 12PSBCh. 10.8 - Prob. 13PSBCh. 10.8 - Prob. 14PSBCh. 10.8 - Prob. 15PSBCh. 10.8 - Prob. 16PSBCh. 10.8 - Prob. 17PSCCh. 10.8 - Prob. 18PSCCh. 10.8 - Prob. 19PSCCh. 10.8 - Prob. 20PSCCh. 10.9 - Prob. 1PSACh. 10.9 - Prob. 2PSACh. 10.9 - Prob. 3PSACh. 10.9 - Prob. 4PSACh. 10.9 - Prob. 5PSACh. 10.9 - Prob. 6PSACh. 10.9 - Prob. 7PSACh. 10.9 - Prob. 8PSACh. 10.9 - Prob. 9PSBCh. 10.9 - Prob. 10PSBCh. 10.9 - Prob. 11PSBCh. 10.9 - Prob. 12PSBCh. 10.9 - Prob. 13PSBCh. 10.9 - Prob. 14PSBCh. 10.9 - Prob. 15PSBCh. 10.9 - Prob. 16PSCCh. 10.9 - Prob. 17PSCCh. 10 - Prob. 1RPCh. 10 - Prob. 2RPCh. 10 - Prob. 3RPCh. 10 - Prob. 4RPCh. 10 - Prob. 5RPCh. 10 - Prob. 6RPCh. 10 - Prob. 7RPCh. 10 - Prob. 8RPCh. 10 - Prob. 9RPCh. 10 - Prob. 10RPCh. 10 - Prob. 11RPCh. 10 - Prob. 12RPCh. 10 - Prob. 13RPCh. 10 - Prob. 14RPCh. 10 - Prob. 15RPCh. 10 - Prob. 16RPCh. 10 - Prob. 17RPCh. 10 - Prob. 18RPCh. 10 - Prob. 19RPCh. 10 - Prob. 20RPCh. 10 - Prob. 21RPCh. 10 - Prob. 22RPCh. 10 - Prob. 23RPCh. 10 - Prob. 24RPCh. 10 - Prob. 25RPCh. 10 - Prob. 26RPCh. 10 - Prob. 27RPCh. 10 - Prob. 28RPCh. 10 - Prob. 29RPCh. 10 - Prob. 30RPCh. 10 - Prob. 31RP
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