Problem
1974 AHSME Problem 23
In the adjoining figure TP and T'Q are parallel tangents to a circle of radius r, with T and T' the points of tangency. PT''Q is a third tangent with T''' as a point of tangency. If TP=4 and T'Q=9 then r is
![[asy] unitsize(45); pair O = (0,0); pair T = dir(90); pair T1 = dir(270); pair T2 = dir(25); pair P = (.61,1); pair Q = (1.61, -1); draw(unitcircle); dot(O); label("O",O,W); label("T",T,N); label("T'",T1,S); label("T''",T2,NE); label("P",P,NE); label("Q",Q,S); draw(O--T2); label("$r$",midpoint(O--T2),NW); draw(T--P); label("4",midpoint(T--P),N); draw(T1--Q); label("9",midpoint(T1--Q),S); draw(P--Q);[/asy]](/static/aops/04fab947ffafd06a13547f83b3774c9162575763.png)
\mathrm{(A)\ } 25/6 \qquad \mathrm{(B) \ } 6 \qquad \mathrm{(C) \ } 25/4 \qquad
\mathrm{(D) \ } \text{a number other than }25/6, 6, 25/4 \qquad
\mathrm{(E) \ }\text{not determinable from the given information}
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