Categories
Beginner

The common triangle

Two semicircles contain a triangle. The centre of the right semicircle is shown. Prove that the triangle is isosceles.

Categories
Beginner

The fried egg

Two concentric circles and two tangents. What is the yellow fraction?

Categories
Beginner

The parallax effect

Two intersecting circles with a triangle that passes through their centres and an intersection point. What’s the angle α?

Categories
Beginner

The purple hat

A circle with three tangents forming an isosceles triangle. Two tangency points are shown. What is the proportion green : red?

Categories
Intermediate

The queen

A cyclic quadrilateral with extended sides and two tangents forming an angle γ. What is γ in terms of α and β?

Categories
Intermediate

Two hemispheres

A triangle with its circumscribed circle and a smaller intersecting circle. The two intersection points and the circumcentre are shown. What’s the proportion red : green?

Categories
Advanced

The new moon

A circle with two tangents, two chords and a secant. Prove that red and green are parallel.

Categories
Intermediate

The wedge

A trapezium with its inscribed circle. Two tangency points are shown. What’s red / blue – yellow / green?

Categories
Intermediate

The fish trap

Two intersecting circles and two common tangents. Prove that α = β.

Categories
Intermediate

Lines in the sand

Two intersecting circles and four chords. Prove that the red chords are parallel.