Question 121820
{{{drawing( 400, 300, -10, 10, -10, 10,
  line( -9, -9, -9, 9 ),
  line( -9,  9,  0, -9 ),
  line( -9, -9,  0, -9 ),
  line( -9, -3,  0, -9),
  line( -9, -8.5,  -8.5, -8.5),
  line( -8.5, -9, -8.5, -8.5),
  locate( -9.5, -2.5, C ),
  locate( -9.5, 9.5, P ),
  locate( -9.5, -9, T ),
  locate(  0.5, -9, R ),
  locate( -4, -9.5, 9 ),
  locate( -4, 1.5, 15 )
  )}}}
OK, I think I've made a representation using the letters that you provided. 
All you need is the Pythagorean theorem. 
Point P and R are on the circle. I don’t show point Q. 
The distance of PR is 15. 
The length of TR is 1/2(18) or 9.
C is the center of the circle. 
PC and CR are radii of the circle. 
There are two right triangles that you use to solve for the radius of the circle. 
Let’s call the radius G since R is already taken.
The first triangle is CRT with sides CT, TR (9), and hypotenuse CR(G). 
Let CT = a. Then,
1.{{{a^2 + 9^2 = G ^2}}} 
The second triangle is PRT with sides PT(G+a), TR(9), and hypotenuse PR(15). 
2.{{{(G+a)^2+9^2=15^2}}}
From 2,
2.{{{(G+a)^2+9^2=15^2}}}
{{{(G+a)^2=15^2-9^2}}}
{{{(G+a)^2=144}}}
{{{G+a=12}}}
{{{G=12-a}}}
Substitute that result into 1.
1.{{{a^2 + 9^2 = G ^2}}} 
{{{a^2 + 81 = (12-a)^2}}} 
{{{a^2 + 81 = 144-24a+a^2}}}
{{{24a=63}}}
{{{a=63/24}}}
{{{a=21/8}}}
From 2,
{{{G=12-a}}}
{{{G=96/8-21/8}}}
{{{G=75/8}}}
The radius of the circle is 75/8.