Three congruent blue circles with a common intersection point. Prove that the red circle through the other intersections is also congruent.
Category: Intermediate
Vanishing point II
Six squares and four coloured triangles. What is red : blue : yellow : green?
Balancing act II
Two squares share a vertex. What’s the angle α?
Mind the steps
Three similar rectangles and a line segment. Express red in terms of blue and green.
In and out
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.
Pop you bubble
A square with a semicircle and a circle of equal radius. Their tangency point is shown. Prove that the red triangle is equilateral.
Wheel of fortune II
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.
In times out
What is the area of the green rectangle, which has sides tangent to the incircle and circumcircle of a triangle with side lengths a, b, c.? (Write the answer as a multiple of a quotient of two elementary symmetric functions in a, b, c.)
Four six four
A regular hexagon and two similar rectangles. What fraction is green?
Eclipsing earth
Two circles with their centres. The quadrilateral ABCD is cyclic and has two sides tangent to the small circle. Prove that BD is also tangent.