10.1

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(3)

cyclic quad. comp. geo (IV Soros Olympiad 1997-98 Correspondence 10.1)

Source:

Two sides of the cyclic quadrilateral

ABCD

AB = a

BC = b

K

is taken on the side

CD

CK = m

. A circle passing through

B

K

D

intersects line

DA

M

, different from

D

AM

geometrycyclic quadrilateral

minutes vs hours angle is 1^o (IV Soros Olympiad 1997-98 R2 10.1)

Source:

Indicate the moment in time when for the first time after midnight the angle between the minute and hour hands will be equal to

1^o

, despite the fact that the minute hand shows an integer number of minutes.

algebrageometry

y=x+|y-3x-2x^2| (IV Soros Olympiad 1997-98 R3 10.1)

Source:

On the coordinate plane, draw a set of points whose coordinates

(x, y)

satisfy the equation

y=x+|y-3x-2x^2|

analytic geometryalgebra