1978 AHSME Problems/Problem 26
Problem
[asy] size(100); real a=4, b=3; // import cse5; pathpen=black; pair A=(a,0), B=(0,b), C=(0,0); D(MP("A",A)--MP("B",B,N)--MP("C",C,SW)--cycle); pair X=IP(B--A,(0,0)--(b,a)); D(CP((X+C)/2,C)); D(MP("R",IP(CP((X+C)/2,C),B--C),NW)--MP("Q",IP(CP((X+C)/2,C),A--C+(0.1,0)))); //Credit to chezbgone2 for the diagram [/asy]
In and
. Circle
is the circle with smallest radius which passes through
and is tangent to
. Let
and
be the points of intersection, distinct from
, of circle
with sides
and
, respectively. The length of segment
is
Solution