Question 831395
{{{drawing(350,250,-27,8,-12.5,12.5,
line(-24.82,0,4.98,0),line(-24.82,0,0,11.12),line(-24.8,0,0,-11.12),
line(5,0,0,11.12),line(4.98,0,0,-11.12),red(circle(4.98,0,12.18)),
line(0.6,9.78,-0.74,9.19),line(-1.33,10.52,-0.74,9.19),
locate(5,1,O),locate(-26,1,P),locate(0.5,11.5,T),locate(0.5,-10,R)
)}}} PT and PR are the tangents from point P to circle O.
The tangents are perpendicular to radii OT and OR, so triangles PTO and PRO are right triangles.
Quadrilateral PTOR is a kite.
Sides PT and PR measure 27.2 cm.
The measure of sides OT and OR is the radius that we want to find.
Angle OPT measures {{{24^o}}}{{{"7 ' 36 ' ' "}}} (half of {{{48^o}}}{{{"15 ' 12 ' ' "}}} ) .
{{{tan(OPT)=OT/PT=0.44788}}} (approximately)
So {{{OT=0.44788*PT=0.44788*(27.2cm)=highlight(12.2cm)}}} (rounded)