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3D Geometry

Source: 1998 National High School Mathematics League, Exam One, Problem 12

March 9, 2020
geometry3D geometrypyramid

Problem Statement

In △ABC\triangle ABC, ∠C=90∘,∠B=30∘,AC=2\angle C=90^{\circ},\angle B=30^{\circ}, AC=2. MM is the midpoint of ABAB. Fold up △ACM\triangle ACM along CMCM, satisfying that ∣AB∣=22|AB|=2\sqrt2. The volume of triangular pyramid A−BCMA-BCM is________.
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