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simelo-math / IMO / 2007 / imo2k7p4_iso.euk

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A B C isosceles
b = bisector(A, C, B)
c = circle(A, B, C)
K = midpoint(segment(B, C))
L = midpoint(segment(A, C))
O = center(c)
% P = intersection(b, line(K, O))
% Q = intersection(b, line(L, O))
C R intersection(b, c)

frame(-4, -4, 8, 6)

draw(A, B, C)
draw(b)
draw(segment(O, K))
draw(segment(O, L))
draw(segment(R, L))
draw(segment(R, K))
draw(c)
% draw(segment(O, Q))
% draw(segment(O, P))

draw("$A$", A, -130:)
draw("$B$", B, -50:)
draw("$C$", C, 130:)
draw("$O$", O, -50:)
% draw("$P$", P, 0.1, -160:)
% draw("$Q$", Q, 0.1, 50:)
draw("$R$", R, -130:)
draw("$K$", K, 50:)
draw("$L$", L, 130:)