Q3 has recently been asked by someone else and solved in another thread.
http://www.mathisfunforum.com/viewtopic.php?id=21271
championmathgirl's method for finding x is much better than mine! see post 11.
Bob
]]>Bob
]]>I've got to out soon so I'll just look at Q1 for the moment.
See diagram. What is the size of the angles at E and F
Bob
]]>2.Equilateral triangle ABC has centroid G. Triangle A'B'C' is the image of triangle ABC upon a dilation with center G and scale factor -2/3. Let K be the area of the region that is within both triangles. Find K/[ABC].
3.A sphere with radius 3 is inscribed in a conical frustum of slant height 10. (The sphere is tangent to both bases and the side of the frustum.) Find the volume of the frustum.
4.In tetrahedron ABCD, \angle ADB = \angle ADC = \angle BDC = 90^\circ. Let a = AD, b = BD, and c = CD.
(a) Find the circumradius of tetrahedron ABCD in terms of a, b, and c. (The circumradius of a tetrahedron is the radius of the sphere that passes through all 4 vertices of the tetrahedron.)
(b) Let O be the circumcenter of tetrahedron ABCD. Prove that \overline{OD} passes through the centroid of triangle ABC.
(The circumradius of a tetrahedron is the radius of the sphere that passes through all four vertices, and the circumcenter is the center of this sphere.)
]]>