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

$PQ=2PT=2 \times 12=24\Rightarrow QW=PQ+PW=24+8=32 \\ \hat{W} \: is \: shared, \widehat{PXW}=\widehat{WQX}\Rightarrow \bigtriangleup PWX\cong \bigtriangleup XWQ \\ \Rightarrow \frac{WX}{QW} = \frac{PW}{WX} \\ \Rightarrow {WX}^{2} = PW.QW = 8 \times 24 = 192\Rightarrow WX = \sqrt{192} = 8 \sqrt{3}\: units$