A right triangle having semicircles along its perpendicular sides and two smaller inscribed circles. Prove that the orange quadrilateral is a square.
Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?
A cyclic quadrilateral and two diagonals. What fraction of its area is blue?
A green quadrilateral of which two sides are tangent to a quarter circle of radius r. What is its area?
A quarter circle with four chords. What is the proportion purple : gold?
Four points A, B, C and D form a quadrilateral. Prove that it is a rectangle if and only if for an arbitrary point P we have PA2+PC2=PB2+PD2.
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?
A quadrilateral covers exactly half of the area of a rectangle. Find the length x in terms of a, b and c.
Two touching circles, two diameters and two common tangents. What is the area of the green quadrilateral in terms of radii x and y?
A square with four quarter circles of which the intersection points are the vertices of a yellow quadrilateral. What fraction of the total area is yellow?