M is any point on the line AB. Squares of side length AM and MB are
constructed and their circumcircles intersect at P (and M). Prove
that the lines AD and BE produced pass through P.
A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?
A quadrilateral inscribed in a unit circle has sides of lengths s1, s2, s3 and s4 where s1 ≤ s2 ≤ s3 ≤ s4.
Find a quadrilateral of this type for which s1= sqrt2 and show s1 cannot be greater than sqrt2.
Find a quadrilateral of this type for which s2 is approximately sqrt3and show that s2 is always less than sqrt3.
Find a quadrilateral of this type for which s3 is approximately 2 and show that s2 is always less than 2.
Find a quadrilateral of this type for which s4=2 and show that s4 cannot be greater than 2.