Maths Olympiad Prep

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Geometry Difficulty 4.5 AIME Find the answer

8. In ABC\triangle A B C, A=70\angle A=70^{\circ}, and DD is a point on side ACA C.

The angle bisector AEA E of A\angle A intersects BDB D at HH, and AHA H

:HE=3:1,BH:HD=5:3: H E=3: 1, B H: H D=5: 3, then C=\angle C=

A number or a short expression. Spacing and $ signs are ignored.

Solution

8.558.55

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.