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In the diagram below, angle PQR=PRQ=STR=TSR, RQ=8, SQ=2.  Find PQ



 

 Jun 3, 2020
 #1
avatar+902 
0

Here is a hint.

 

Using angle equalities what type can your prove that TSR and PQR are?

 

As this is an AoPS question please do not post full solutions, but hints are ok.

 Jun 3, 2020
 #2
avatar+71 
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TY! THIS HELPED A LOT

 Jun 3, 2020
 #5
avatar+1128 
0

What helped a lot?

jimkey17  Jun 4, 2020
 #6
avatar+71 
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The hint!

violetzhang07  Jun 4, 2020
 #3
avatar+1322 
+1

This diagram may help you solve this geometry problem.  smiley

 

QR = QT = 8

 

XT = QS = 2

 

XY = TL = sqrt( QT² - QL² )

 

TR = QX = sqrt ( XY² + QY² )

 

You can take it from here;  it's easy.  laugh

 

 Jun 3, 2020
edited by Dragan  Jun 3, 2020
edited by Dragan  Jun 3, 2020
edited by Dragan  Jun 4, 2020
 #4
avatar+71 
0

tysm!!! laughlaugh

violetzhang07  Jun 4, 2020

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