Problems in Geometry (2)
1. Given a rectangle ABCD prove that |P A|2 + |P C |2 = |P B |2 + |P D|2 for any point P.
2. Given an acute angled positively oriented triangle ABC, let O and H be the circum
center and the orthocenter of ABC, respectively. Let AH
Problems in Geometry (7)
1. Let be an ellipse with foci F, F . If the tangent lines at A, B intersect in P ,
prove that P F AB i F AB . 1
2. Let be an ellipse with foci F, F . Let t, t be the tangents to which intersect in P .
If H, H are respectively the
Problems in Geometry (6)
1. What is the locus of a point whereof the power with respect to a xed circle is a
constant ?
2. Compute the power of the point P (x0 , y0 ) with respect to the circle x2 + y 2 +2ax +2by +
c = 0. Write down the equation of the ra
Problems in Geometry (1)
1. In a triangle ABC with orthocenter H and circumcircle O prove that
< BAH =< OAC .
1
2. Let ABC be a triangle with orthocenter H in which AH, BH, CH meet BC, CA, AB
in D, E, F respectively. Prove that
HA HD = HB HE = HC HF.
2
3.
Problems in Geometry (8)
1. (A) What is the image of the line 2x + y = 2 under Tr[1,3] ?
(B) What is the image of the line x = 1 under Rot(0, 0), /4) ?
(C) What is the image of the line x + y = 1 under Refk , where k is the line y = 2x ?1
2. (A) Let P, Q
Problems in Geometry (5)
1. Given a circle , consider points P, C, D and let [A, B ] be a diameter of . Prove
that the Simson line of P with respect to the triangle ACD is perpendicular to the Simson
line of P with respect to the triangle BCD.1
2. Given a
Problems in Geometry (4)
1. Consider a quadrangle ABCD with points P, Q, R, S, T on BD, AB, AD, CB, CD
respectively. Prove that if P, Q, R are collinear and P, S, T are collinear, then the lines
1
QS, RT, AC are concurrent.
2. The following is a problem b
Problems in Geometry (3)
1. Given a triangle ABC, let A be the midpoint of [B, C ] and consider Y CA cfw_C, A,
Z AB cfw_A, B such that BY and CZ meet on AA . Prove that Y Z is parallel to BC.1
2. Given a triangle ABC, consider P BC cfw_B, C , Q CA cfw_C,