A triangle containing three tangent semicircles with diameters a, b and c. Three line segments pass through the red tangency points. What is the triangle perimeter?
Month: September 2022
The grazing shot
A parabola and its directrix in red. Two tangents intersect at a point on the directrix. What’s the angle α?
The iron curtain
A parallelogram ABCD with a circle and a diameter CE. Prove that point E is the orthocentre of triangle ABD.
Worlds colliding
Two intersecting circles and a circle passing through both their centres and their intersection points. What’s the angle α?
The common triangle
Two semicircles contain a triangle. The centre of the right semicircle is shown. Prove that the triangle is isosceles.
At navel level
Two equilateral triangles share a vertex. The centre of the larger one is aligned with the midpoint of a side of the smaller one. What is green : red?
Sharing is caring
Three equilateral triangles and three shared vertices. What’s the proportion blue : green?
The fried egg
Two concentric circles and two tangents. What is the yellow fraction?
Lopsided
The apex of a parabola is the shared vertex of two rectangles. Proof that the rectangles are similar.
Harmonic proportions
A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.