Two rods of length x and y are connected by two strings with a knot exactly halfway. The rods are placed parallel both with uncrossed and crossed strings. The distance between the knots is measured as a and b respectively. Express x and y in terms of a and b.
The tangency points of two tangents of a circle are connected. Three perpendiculars are drawn from a point on the circle, of which two have a given length. What’s the proportion red : yellow?
The midpoints of the hypotenuse of a right triangle and a line segment are connected. What is the length x?
A circle with four chords. What is the segment length x in terms of lengths a, b and c?
Three semicircles of which two centres are connected to corner points. What is the area X in terms of A and B?
An equilateral triangle with a circle tangent to two sides. The vertices are the tangency points. What is the length proportion of line segments x : y?
Three squares and four extended sides. What is the yellow area X in terms of blue and green areas A and B?
Two touching circles, two diameters and two common tangents. What is the area of the green quadrilateral in terms of radii x and y?
Three triangles have the same base. What is the top angle γ of the middle one in terms of the other ones α and β?
Two triangles share a side. What’s the angle β?