Task 627
Task 627: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. In triangle $ABC$, angle $ACB$ is 50 degrees, and angle $CBA$ is 70 degrees. Let $D$ be the foot of the perpendicular from $A$ to $BC$, $O$ the center of the circle circumscribed about triangle $ABC$…
The task
In triangle $ABC$, angle $ACB$ is 50 degrees, and angle $CBA$ is 70 degrees. Let $D$ be the foot of the perpendicular from $A$ to $BC$, $O$ the center of the circle circumscribed about triangle $ABC$, and $E$ the other end of the diameter which goes through $A$. Find the angle $DAE$, in degrees. [asy] unitsize(1.5 cm); pair A, B, C, D, E, O; A = dir(90); B = dir(90 + 100); C = dir(90 - 140); D = (A + reflect(B,C)*(A))/2; E = -A; O = (0,0); draw(Circle(O,1)); draw(A--B--C--cycle); draw(A--D); draw(A--E,dashed); label("$A$", A, N); label("$B$", B, W); label("$C$", C, SE); label("$D$", D, SW); label("$E$", E, S); dot("$O$", O, dir(0)); [/asy]