Circle Geometry Problem

[Tarmac27]

Hello all,

I have come across this circle geometry problem and I am having a difficult time trying to prove what is asked.

I have tried many approaches and I'm assuming that you need to first show that XS = 4cm then have RHS congruency between XPS and PRS but I just cant find a way to show that XS is 4cm. Is there a different way I am missing?

Anything helps,

Thanks.

 

[lex]

[MATH]\bigtriangleup[/MATH]RQX is similar to [MATH]\bigtriangleup[/MATH]PMQ
scale factor is 2, since PM=2, QR=4
[MATH]\therefore[/MATH] XR = 2[MATH]\times[/MATH]PQ
= 2[MATH]\times[/MATH]4
= 8

 

[Tarmac27]

ah yes, that pretty much solves it

Thank you for that makes a lot more sense now.

 

[lex]

grand