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?
Categories
At navel level
Category: Intermediate
Categories
Sharing is caring
Three equilateral triangles and three shared vertices. What’s the proportion blue : green?
Categories
Lopsided
The apex of a parabola is the shared vertex of two rectangles. Proof that the rectangles are similar.
Categories
Harmonic proportions
A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.
Categories
The piercing
An equilateral triangle containing a right triangle and a line segment. What fraction is pink?
Categories
The crazy quilt
A parallelogram is divided into several areas. What is the area X of the blue trapezium?
Categories
The common focus
A parabola, its symmetry axis and a tangent. Yellow connects the focus to the intersection point. Red connects the focus to the tangency point. What’s yellow : red?
Categories
Under the volcano
A square containing a right isosceles and an equilateral triangle. What’s the angle α?
Categories
The Pisa experiment
Four squares and an altitude to the top vertex form a right yellow traingle. What is the proportion yellow : green?
Categories
The queen
A cyclic quadrilateral with extended sides and two tangents forming an angle γ. What is γ in terms of α and β?