Categories
Intermediate

The Arcus arcade

A semicircle and an inscribed circle. Prove that the circle centre is on the parabola.

Categories
Intermediate

The Suresh similarity

Two squares and a rectangle. Prove that the red triangles are similar.

Categories
Intermediate

A new slant

Two squares and a slanted rectangle share three vertices. What is the total area?

Categories
Intermediate

The helmet

A circle, a semicircle, a chord and an altitude. What is the length of the latter in terms of a and b?

Categories
Intermediate

Equilibrium

Three squares and a circle. The areas of the squares are given. What is the area of the circle?

Categories
Intermediate

The fish bowl

A circle with an inscribed triangle, a tangent and two bisected angles. What is the length proportion of the red and green line segments?

Categories
Intermediate

House of the rising sun

A semicircle, a circle, a square and an equilateral triangle. The two points are the tangency point and the semicircle centre. What fraction of the total area is yellow?

Categories
Intermediate

Il tricolore

Two squares share two vertices. A line segment connects two other vertices, forming the base of three triangles. What is the proportion green : white : red?

Categories
Intermediate

The intersection

Two intersecting circles. Prove that the three blue line segments are of equal length.

Categories
Intermediate

All the marbles

A circle containing eight touching circles. Circles of equal colour are congruent. What fraction of the total area is coloured?