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The two circles below are externally tangent. A comon external tangent intersects line PQ at R. Find QR.

 

asy]
unitsize(0.3 cm);

pair A, B, C, D, E;

A = (0,0);
B = (8,0);
C = (20,0);
D = intersectionpoint(Circle(A,5), arc((A + C)/2, abs(A - C)/2, 0, 180));
E = intersectionpoint(Circle(B,3), arc((B + C)/2, abs(B - C)/2, 0, 180));

draw(Circle(A,5));
draw(Circle(B,3));
draw(A--D);
draw(B--E);

dot("$P$", A, SW);
dot("$Q$", B, S);

label("$8$", (B + E)/2, W);
label("$10$", (A + D)/2, W);
[/asy]

 Jan 9, 2023

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