Math 427, Midterm 1.
Your name: 1. Prove that three angles in a triangle sum up to 180 .
2. Give a proof of Pythagorean theorem using similar triangles.
3. Let two circles and intersect at A and B. Let CD be a chord on . Let AC and BD intersect again
Math 427, Midterm 3. Your name: Each problem costs 20 points. 1. Suppose A, B, C and D are four points on projective plane, no three of which are colinear; and suppose A , B , C and D are another set of four points on projective plane, no three of which a
Math 427, Midterm 2.
Your name: Each problem costs 20 points. 1. Let ABC be a triangle on the plane with cirumradius R. Show that b c a = = = 2R. sin sin sin
2. Suppose ABC is a triangle on the unit sphere. Show that the area of triangle is given by |
Math 427, Quiz 7.
Your name: 1. Give a triple pf real numbers (a, b, c) which are not projective coordinates of any point in P2 .
2. Which of the following pairs of points (in projective coordinates) are equal? (i) (1, -1, 1) and (-1, 1, -1) (ii) (-1, 1,
Math 427, Quiz 6.
Your name: 1. In a ABC with right angle at C and legs a = b = 1 one choose points X and Y correspondingly on legs BC and AC such that |CX| = 2/3 and CY = 1/3. Let P be a point of intersection of lines AX and BY and Z be the point of inte
Math 427, HWA 11, Solutions.
1. Let A, B, C, D be points on one line. Show that (A, B; C, D) + (A, C; B, D) = 1. Solution: Let a, b, c, d be coordinates of A, B, C, D correspondingly then (A, B; C, D) = and (A, C; B, D) = Therefore (A, B; C, D) + (A, C; B