Problem
1983 AHSME Problem 30
Distinct points A and B are on a semicircle with diameter MN and center C. The point P is on CN and \angle CAP = \angle CBP = 10^{\circ}. If \stackrel{\frown}{MA} = 40^{\circ}, then \stackrel{\frown}{BN} equals
![[asy] import geometry; import graph; unitsize(2 cm); pair A, B, C, M, N, P; M = (-1,0); N = (1,0); C = (0,0); A = dir(140); B = dir(20); P = extension(A, A + rotate(10)*(C - A), B, B + rotate(10)*(C - B)); draw(M--N); draw(arc(C,1,0,180)); draw(A--C--B); draw(A--P--B); label("$A$", A, NW); label("$B$", B, E); label("$C$", C, S); label("$M$", M, SW); label("$N$", N, SE); label("$P$", P, S); [/asy]](/static/aops/6f8eeadd8cd1dc376957cf77a425565771406dee.png)
\textbf{(A)}\ 10^{\circ}\qquad \textbf{(B)}\ 15^{\circ}\qquad \textbf{(C)}\ 20^{\circ}\qquad \textbf{(D)}\ 25^{\circ}\qquad \textbf{(E)}\ 30^{\circ}
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