# Circle Geometry Problem

#### Tarmac27

##### New member
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

##### Junior Member
$$\displaystyle \bigtriangleup$$RQX is similar to $$\displaystyle \bigtriangleup$$PMQ
scale factor is 2, since PM=2, QR=4
$$\displaystyle \therefore$$ XR = 2$$\displaystyle \times$$PQ
= 2$$\displaystyle \times$$4
= 8

#### Tarmac27

##### New member
ah yes, that pretty much solves it

Thank you for that makes a lot more sense now.

grand