The racer at A is running counter-clockwise around the inside of the outer purple circle, with a “shadow racer” B following behind, related by the three chords that are tangent to the inner orange circle. Does the shadow B ever catch up with A?
Two tangent circles and two green tangents. The three tangency points are shown in black. Prove that the blue line segment is a common tangent.
A regular hexagon, a square and an equilateral triangle. Show that the top vertex of the triangle is on the hexagon circumcircle.
Identical circles have their centers aligned as shown, with the middle circle inscribed in a triangle. Show that the outer circles can be made tangent to the green circumcircle if the red axis is rotated correctly.
Three congruent blue circles with a common intersection point. Prove that the red circle through the other intersections is also congruent.
A green line connects two points of tangency of a triangle to its incircle. A red line is the angle bisector at a vertex, and an orange line connects the midpoints of two sides. Show that the three lines are concurrent.
An obtuse triangle, of which α is the obtuse angle, with its incircle, two cevians and two tangents. Find a relation between α and β.
Two quarter-circles fit inside a square, and five circles fit inside the overlapped region, centred. What is the ratio of the (straight line) segment lengths red to blue? (The segments connect to points of tangency.)
A square with a semicircle and a circle of equal radius. Their tangency point is shown. Prove that the red triangle is equilateral.
A triangle with its incircle and three cevians. The tangency points and incentre are shown. Find the relation between the angles α, β and γ.