Question

Line WX is tangent to circle T at point X. Line WT intersects the circle at points P and Q. The radius of circle T is 12 units and WP = 8 units. What is WX?​

Answer 1

`PQ=2PT=2 * 12=24\Rightarrow QW=PQ+PW=24+8=32 \\ \hat{W} \: is \: shared, \widehat{PXW}=\widehat{WQX}\Rightarrow \bigtriangleup PWX\cong \bigtriangleup XWQ \\ \Rightarrow (WX)/(QW) = (PW)/(WX) \\ \Rightarrow {WX}^(2) = PW.QW = 8 * 24 = 192\Rightarrow WX = √(192) = 8 √(3)\: units`