A semicircle and an inscribed circle. Prove that the circle centre is on the parabola.
Category: Intermediate
The Suresh similarity
Two squares and a rectangle. Prove that the red triangles are similar.
A new slant
Two squares and a slanted rectangle share three vertices. What is the total area?
The helmet
A circle, a semicircle, a chord and an altitude. What is the length of the latter in terms of a and b?
Equilibrium
Three squares and a circle. The areas of the squares are given. What is the area of the circle?
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?
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?
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?
The intersection
Two intersecting circles. Prove that the three blue line segments are of equal length.
All the marbles
A circle containing eight touching circles. Circles of equal colour are congruent. What fraction of the total area is coloured?