3
Part of 2004 Pan African
Problems(2)
Equal sum
Source: Pan African 2004
10/4/2005
One writes 268 numbers around a circle, such that the sum of 20 consectutive numbers is always equal to 75. The number 3, 4 and 9 are written in positions 17, 83 and 144 respectively. Find the number in position 210.
Perpendicular if and only if Centre
Source: Pan African 2004
10/4/2005
Let be a cyclic quadrilateral such that is a diameter of it's circumcircle. Suppose that and intersect at , and at , and at , and let be a point on . Show that is perpendicular to if and only if is the midpoint of .
geometrycircumcirclecyclic quadrilateral