The death dish is semicircular, with point C for aiming the ray, which bisects the green and red lines. The maximum range of the death ray is the sum of the red and green lengths. What is the locus of the maximum point X as C varies?
Three squares and three line segments, What is the angle α?
Two tangent circles, a common tangent and a perpendicular line segment inside a triangle. Prove that the three green points are collinear.
Two squares and an extended diagonal. What is red : blue?
A green kite BDHA shares the vertices D, H with a circle (DHJL). DA intersects the circle in the points D and J. The side HA, extended, meets the circle at L. Show that the angle between LJ and BD is the same as between AD and AH: is η = ε?
Two squares, one of which has an extended side. What is the angle α?
Fixed point C, at distance x from the center of a unit semicircle. The rectangle varies with angle α from 0 to 90 degrees. What is the radius of the arc traced by the corner point G. Is the arc concentric with the green arc?
Two squares and a circle. What is red : green : blue?
Two congruent tangent circles and a rectangle with an extended side. What is yellow : red?
Two circles meet orthogonally at points Q and R. The blue radius AM=3 and MP = 2. What is the length of the red segment PC?
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